[Formendacil]

While I incline to agree with your answer, that Gandalf would not have returned--at least not as Gandalf the White, and probably not returned at all, it strikes me as fascinating to speculate what if Gandalf the White HAD appeared.

Because by this time, though no one knew it, Saruman was well on the path to evil. Or, rather, let me correct myself: no one, presumably, no one among the Wise or in the West knew. Eru presumably did, and when Gandalf actually returns in The Lord of the Rings, it is because Eru sends him back. On the assumption that the Allfather is omniscient (which is admittedly borrowing from "Real World" philosophy but I think it's safe), he would have known Saruman had turned... and thus that Gandalf was still needed, more than ever.

Of course, with a bent for Divine Providence in my system, I'm willing to say that Eru acted through the Eagles--or perhaps, more convolutedly, since Eru is undoubtedly intelligent enough for convolutions--Eru acted through the Valar acting through the Eagles, who happen to show up just in time. Knowing what is to come, this strikes me as having the same sort of divine serendipity to it as Bilbo finding the Ring--Gandalf was meant to fall saving Frodo from the Balrog, returning just in time to fight Saruman and Sauron at the only moments when an unveiled Istar would have been "permitted."

However, if we engage in some counter-factualism, the appearance of Gandalf the White on the scene--had Eru gone for it--80 years early would have messed with Middle-earth rather strongly. A lot depends, of course, on whether or not Gandalf's death was successful. I'm inclined to think so, since it worked the second time, but there's no guaranteeing Thorin & Co. would have made it all the way to Erebor. If they had, there's no apparent reason things couldn't have gone as planned--Gandalf's contribution effectively ends with Beorn sending them off--but the Battle of the Five Armies could have been disastrous: the Elves and Dalemen decimate the Dwarves, and vice versa, and the orks arrive just in time to destroy the tired remnants. Even if the Eagles show up, perhaps it's to do nothing more than help a few sorry survivors escape--including, I would hope, an invisible Bilbo.

Gandalf the White, perhaps, would turn up about now, hopefully having more knowledge about the Ring, given that Eru was involved. Even so, he has to get Bilbo to Mt. Doom and either hope the Hobbit can let it go himself (which, one remembers, he did manage in LotR--albeit in Bag-End with Gandalf's help) or else he'll have to chuck Bilbo in whole. Unpleasant all around, and perhaps Gandalf falls morally.

But this assumes Gandalf can go at all. This might be a case of delegation--perhaps a band of survivors from the disastrous Battle of the Five Armies becomes the Fellowship of the Ring: Bard replaces Aragorn, Legolas tags along fatherless, and a dour trio of Glóin, Fíli, and Balin--all that's left of Thorin & Co. Meanwhile, Gandalf leaves what's left of the three "good" armies under the care of Dáin or somebody, while orks continue to overrun Wilderland, and both Sauron and Saruman are alerted (via palantír or spy... I doubt they failed to watch the Battle of the Five Armies or note Gandalf's reappearance), and now there's war against Rohan and Gondor and Lórien. Admittedly, Sauron's not prepared--he's still in Dol Guldur, and a long way from building up his War of the Ring forces, but he's got forces aplenty, and the Nazgûl can still strike Gondor from Minas Morgûl.

The decisive difference is that Rohan probably wouldn't face much of a threat in Saruman, who would still be early along in building his armies, though perhaps orks from the Misty Mountains would compensate. If Saruman was a force at all, perhaps it would be in driving a wedge between Gondor and Rohan (he's technically the Gondorian ward of Orthanc, after all). Much depends who was on the throne in Rohan and Gondor--but I don't think they were remarkable men yet. If it was Fengel in Rohan, certainly not, and I seem to recall that Turgon was an old man near the end of his life when Sauron returned to Mordor from Dol Guldur. Alas, I don't have my books with me.

All in all... yeah... I got a little carried away. It's a fascinating idea, though. And, confound it, that looks like a really awesome RPG idea...