[Boromir88]

Possible; although I would have several "buts" to it. First, I am pretty sure Gríma did not just randomly walk between Isengard and Edoras, certainly not officially (otherwise he'd be so suspicious, even if he'd used to do it only before Saruman openly became the enemy! And Gandalf proclaims his revelation that Saruman has bought Wormtongue as a big thing and it seems to e.g. dawn upon Éomer only in that moment), I always imagined it the way that Gríma sneakily traveled to Isengard from time to time when he was on a "holiday" or somesuch ("sir, I'm going to take a week off, I have to visit my old grandmother in the Westfold"). So there is no way he could deliver any official message in Saruman's name.~Legate

Your "buts" sound more likely than Grima bringing Saruman's "offer" to Théoden. Grima's deception was more a work of a subtle counselor, not acting as an emissary of Saruman. I think when Théoden's health begins failing, and Grima gets a stronger grip over him (as Faramir Jones points out the UT says this was in TA 3014), Grima may have been bolder in outwardly supporting Saruman, but as far as making Saruman's initial offer "long ago," I think you're right, it wouldn't have come from Grima.

Let's try to put together a timeline. We know Saruman is given the keys to Orthanc and runs Isengard during the Steward, Beren's, and King Frealaf's reign:

It can thus be readily understood that when Saruman offered to take command of Isengard and repair it and reorder it as part of the defenses of the West he was welcomed both by King Frealaf and by Beren the Steward. So when Saruman took up his abode in Isengard, and Beren gave him the keys of Orthanc, the Rohirrim returned to their policy of guarding the Fords of Isen, as the most vulnerable point in their western frontier.~UT: The Battles of the Ford of Isen (Appendix)

And the timeline in the Lord of the Rings notes specifically it was 2759 that Saruman was given the keys to Orthanc. Rohan was having a lot of trouble with Dunlendings. Isengard was under control of Gondor, but Gondor didn't pay too much attention to it, leaving Isengard in control of a hereditary Lord. It's noted those lords became more and more mixed with the Dunlendings and were more sympathetic to them, perceiving the Rohirrim as the aggressive invaders. Isengard and Aglarond are key forts to the defenses of both Rohan and Eriador. This was figured out when Dunlendings took control of Isengard (TA 2710) and it wasn't until the Long Winter (TA 2758-59) they were "starved out and captitulated to Frealaf" (ibid)

There can be little doubt that Saruman made his offer in good faith, or at least with good will towards the defense of the West, so long as he himself remained the chief person in that defense, and the head of its council. He was wise, and perceived clearly that Isengard with its position and its strength, natural and by craft, was of utmost importance. The line of the Isen, between the pincers of Isengard and the Hornburg, was a bulwark against invasion from the East (whether incited and guided by Sauron, or otherwise), either aiming at encircling Gondor or at invading Eriador. But in the end he turned to evil and became an enemy; and yet the Rohirrim, though they had warnings of his growing malice towards them, continued to put their main strength in the west at the Fords, until Saruman in open war showed them that the Fords were small protection without Isengard and still less against it.~ibid

A couple important things from this. Isengard's strategic importance to either invading Eriador, or invading Rohan and encircling Gondor. And I found it interesting that Saruman initially offered (in good faith) to take Isengard for the defense of the West "so long as he himself remained the chief person in that defense, and the head of its council." Anyway, with Saruman in Isengard by the year 2759, the Rohirrim believed they had a trusted ally that would not allow the Dunlending invasions into Rohan again. So they withdrew and went back to focusing on defending the Fords and Aglarond.

In TA 2851:

The White Council meets. Gandalf urges an attack on Dol Guldur. Saruman overrules him. Saruman begins to search near the Gladden Fields.~Lord of the Rings: Appendix B

This I believe would have been under King Folca's reign. Rohan was finally recovering their strength. Saruman begins to perhaps have plans that aren't entirely in "good faith towards the defenses of the West," but since he was able to overrule Gandalf at the Council, I'd say he would still feel the "chief person" at this time and thus wouldn't have ill-will towards Rohan...yet.

TA 2953:

Last meetings of the White Council. They debate the Rings. Saruman feigns that he has discovered that the One Ring has passed down Anduin to the Sea. Saruman withdwards to Isengard, which he takes as his own, and fortifies it. Being jealous and afraid of Gandalf he sets spies to watch all his movements; and notes his interest in the Shire. He soon begins to keep agents in Bree and the Southfarthing~ibid

This would have been right at the beginning of King Thengel's reign, which as quoted in an earlier post it's said Saruman began giving trouble to Rohan. I agree with Faramir Jones that at this point when Saruman declares himself Lord of Isengard and fortifies it, he wouldn't have been travelling out of Isengard (or very far from it).

Fengel wasn't a well liked King, which is why Thengel left and went to Gondor, married a woman of Gondor and the Rohirrim basically begged Thengel to come back and be their king as Fengel's only male heir when Fengel died. It's said under Thengel in Kings of the Mark he did so "unwillingly" but still proved to be a good and wise King. I'm not sure if the political situation in Rohan is described too much during this time, but it's right around the time that Saruman has turned traitor (even though this isn't known until much later). In 2953, Théoden would have only been 5, but it wouldn't surprise me if Saruman started devising plans to destabilize Rohan politically at this time. Fengel wasn't a good king, Thengel unwillingly returned. Théoden was his only male heir and in his youth this is what's said of Théoden:

In the days of Théoden there was no man appointed to the office of First Marshal. He came to the throne as a young man (at the age of thirty-two), vigorous and of martial spirit, and a great horseman. If war came, he would himself command the Muster of Edoras; but his kingdom was at peace for many years, and he rode with his knights and his Muster only on exercises and in displays; though the shadow of Mordor reawakened grew ever greater from his childhood to his old age...When Théoden became, as it seemed, prematurely old, this situation continued, and there was no effective central command: a state of affairs encouraged by his counselor Grima. The King, becoming decrepit and seldom leaving his house, fell into the habit of issuing orders to Hama, Captain of his Household, to Elfhelm, and even to the Marshals of the Mark, by the mouth of Grima Wormtongue. This was resented, but the orders were obeyed, within Edoras.~Battles of the Fords of Isen (Appendix)

I might not have needed to go through all of this, but I was trying to put together a timeline of when Saruman was given control of Isengard, when he turned traitor, and how this fit with the politics in Rohan. There is a time here, from Fengel's reign to Théoden, where it doesn't look like Rohan is politically stabile, and is weakened, which Saruman tried to capitalize on and completely destabilize Rohan by the events in the Lord of the Rings.

And Théoden becoming King at a young age (32) to his noticeably failing health (66) gives Saruman 34 years (possibly even longer, before Théoden was King) to try to make an offer to the young Marshal (or King) that Legate talks about. Théoden in his youth was a "vigorous and martial" spirit, and he was Thengel's only male heir. I can see Saruman "long ago" making an offer to the young King about an alliance. In an effort to either win over the Rohirrim to his side, or having failed that, destabilize Rohan by using Grima.

Ah well...now that I've finally gotten to the Voice of Saruman chapter:

"But come now," said the soft voice. "Two at least of you I know by name. Gandalf I know too well to have much hope that he seeks help or counsel here. But you, Théoden Lord of the Mark of Rohan, are declared by your noble devices, and still more by the fair countenance of the House of Eorl. O worthy son of Thengel the Thrice-renowned. Why have you not come before, and as a friend? Much have I desired to see you, mightiest king of western lands, and especially in these latter years, to save you from the unwise and evil counsels that beset you! Is it yet too late? Despite the injuries that have been done to me, in which the men of Rohan, alas! have had some part, still I would save you, and deliver you from the ruin that draws nigh inevitably, if you ride upon this road which you have taken. Indeed I alone can aid you now."~The Voice of Saruman

Bolding for my emphasis. So, it's at least clear from both Saruman's words and Théoden's that the two never met face-to-face before (although, Saruman still could have sent a message or emissary with an offer). Then he says Théoden's road (side with Gandalf and aid Gondor) will lead to ruin, and an alliance with Saruman alone can save him.

Therefor, it wouldn't surprise me when Saruman started causing trouble to Rohan (beginning of Thengel's reign), even though if early on in Théoden's reign their appeared to be peace, to try to convince Théoden that history was repeating itself and Théoden needed an alliance with Saruman. I can see Saruman's offer he made "long ago" and he made again here, being something like: "I'm seeing the wild Dunlendings coming back and encroaching on your lands, as has happened before. A shadow is returning to Mordor and harassing Gondor again, you won't get any help from them. Besides in those earlier troubles they left Isengard in command of someone who was sympathetic and allowed the wildmen to invade. Fortunately, I'm in Isengard now and offer my friendship and help to handle the Dunlanders. You won't get aid from Gondor. I was placed in Isengard to be the commander in the defenses of the West, Gondor has been without a king for centuries, making you, Théoden, the mightiest King in the western lands. I have long foreseen this war and only friendship with me can save you."