Speaking of Sauron's possible defeat at the hands of one of the Wise, I'd first take a look at how he may have been defeated as see in the history of Arda.
First, a look at letter #211:
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Ar-Pharazôn, as is told in the 'Downfall' or Akallabêth, conquered a terrified Sauron's subjects, not Sauron. Sauron's personal 'surrender' was voluntary and cunning[1]: he got free transport to Numenor! He naturally had the One Ring, and so very soon dominated the minds and wills of most of the Númenóreans.
[1] Note the expression III p. 364 [2nd edition p. 365] 'taken as prisoner'.
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So this apparent first precedent actually was not a precedent at all, but something different. The only occasions on which Sauron had truly been defeated where, as is said in the above letter:
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Sauron was first defeated by a 'miracle': a direct action of God the Creator, changing the fashion of the world, when appealed to by Manwë: see III p. 317. Though reduced to 'a spirit of hatred borne on a dark wind'
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So when Númenor was destroyed. And:
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Sauron was, of course, 'confounded' by the disaster, and diminished (having expended enormous energy in the corruption of Númenor). He needed time for his own bodily rehabilitation, and for gaining control over his former subjects. He was attacked by Gil-galad and Elendil before his new domination was fully established.
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The thing is, by the time of the War of the Ring, none of these two precedents could be repeated. Eru would not intervene that much (ok, he did a bit, but not on the scale of the destruction of an island) and also he had fully established his domination, unlike during the attack of the Last Alliance.
Considering the relative power of Gandalf with the Ring and Sauron without I most like to take a look at letter #144:
First, Tolkien explains that neither Frodo nor any other mortal, not even Aragorn could ever be able to defeat Sauron with the Ring. He then reffers to the Wise, saying:
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Of the others only Gandalf might be expected to master him – being an emissary of the Powers and a creature of the same order, an immortal spirit taking a visible physical form. In the 'Mirror of Galadriel', 1381, it appears that Galadriel conceived of herself as capable of wielding the Ring and supplanting the Dark Lord. If so, so also were the other guardians of the Three, especially Elrond. But this is another matter. It was part of the essential deceit of the Ring to fill minds with imaginations of supreme power. But this the Great had well considered and had rejected, as is seen in Elrond's words at the Council. Galadriel's rejection of the temptation was founded upon previous thought and resolve. In any case Elrond or Galadriel would have proceeded in the policy now adopted by Sauron: they would have built up an empire with great and absolutely subservient generals and armies and engines of war, until they could challenge Sauron and destroy him by force. Confrontation of Sauron alone, unaided, self to self was not contemplated. One can imagine the scene in which Gandalf, say, was placed in such a position. It would be a delicate balance. On one side the true allegiance of the Ring to Sauron; on the other superior strength because Sauron was not actually in possession, and perhaps also because he was weakened by long corruption and expenditure of will in dominating inferiors. If Gandalf proved the victor, the result would have been for Sauron the same as the destruction of the Ring; for him it would have been destroyed, taken from him for ever. But the Ring and all its works would have endured. It would have been the master in the end.
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So the general idea that this quote gives is firstly that more or less Gandalf alone could ever have hoped to replace Sauron.
Elrond and Galadriel would have built up large armies and attacked Mordor, but victory seems to have been a plausible option at best, since a direct encounter with Sauron would have been fatal and that after probably all the dreams of replacing Sauron were a consequence of the Ring's own influence. So, the wisest and strongest of Elves had a dim chance at best.
Gandalf, on the other hand would have had a delicate balance of power if he encountered Sauron. The thing is Tolkien names no victor here, so one can speculate at best about Gandalf's chances to become the next Dark Lord.
So, all in all, it appears that noone truly could have challenged Sauron and won, except Gandalf perhaps.
And to return to the thread at hand, there is no mention of Saruman in this whole passage - showing that for Tolkien Saruman as a new Dark Lord was not even a possibility. So again, why would he then hope to be accepted by Sauron?
And, talking about the attack on Dol Guldur, it appears to have actually been planned by Sauron, so Saruman played a minor part there at best.
Btw, I apologize for myself lacking a sense of humor, I actually believed you meant the "Son of Saruman" idea as a viable possibility.
And as much as I enjoy speculating, as I did in the other thread, I believe that in some cases there simply is not enough supporting it. And I now for example feel the same about the idea of the old man near Fangorn having been a ghost or an image of Gandalf after having seen the quotes from HoMe which clearly pointed towards Saruman as a culprit.