This is a fascinating question, and there are some intriguing possibilities, most of which involve asking other difficult questions. My short answer is "no", for the following reasons.
1) According to Gandalf and Elrond at varying times in LOTR, the ring is described as being Sauron's alone, having been drawn from a repository of power that was native to him in his beginning. While the corrupting power of the ring is clearly illustrated in the cases of Isildur, Smeagol, Bilbo, and Frodo, and its tempting power illustrated in the cases of Gandalf, Saruman, Galadriel and Samwise, there is nothing that states that the full inherent power of the ring would actually be available to any of those potential users. While Gandalf does explain that the ring gives power according to the user's potential or "stature", this has never actually been tested (with the possible exceptions of Smeagol and Bilbo, who never progress beyond the ring's more basic attributes of invisibility and long life). Isildur seemed to have tried, and Unfinished Tales suggests that he was not able to bend the ring to his will and in LOTR, the post-Battle of the Pelennor Fields council imagines that Sauron would scoff at Aragorn attempting to do so. Both Galadriel and Samwise imagine that they can overthrow Sauron with the use of the ring, but this is likely a method by which the ring attempts to reveal itself to Sauron. The fact that Gandalf, who fears to use the ring, and Saruman, who desires it, are both of the same angelic order as Sauron adds weight to the argument that the ring would be usable in all its power by other Maiar and, therefore, they could be vulnerable. However, the balance of the evidence seems to point to the ring's full potential being available only to Sauron, with the domination and control of other minds being its primary attribute. The Valar, being of a higher level in the angelic order, would not likely be tempted by the ring, it being merely a part of Sauron's original, native power, which would be far below what they would themselves possess. In the same way that the first rings forged by the elves of Eregion were "trifles" and "mere essays in the craft", but perilous for mortals, Sauron's ring would likewise be considered a trifle by the Valar.
2) Depending on where you stand on the identity of Tom Bombadil, we may have already seen the effect of the ring on a Vala. I am not resurrecting that unanswerable question, but if Tom is indeed a Vala, we can see when the hobbits visit his house that the ring has no visible effect on him when he places it on his little finger, and he can seemingly make it disappear for a moment (though that may have been a simple parlor trick). Gandalf knows more than anyone who Bombadil is, and argues against giving him the ring for safekeeping, noting that he would likely lose it or throw it away, such things having no particular hold on his mind. That might indicate that he is not in the "position" to concerned with matters of grave importance to men, elves, and even Maiar, suggesting that he might be operating on a higher sphere.
3) An interesting point to consider is whether or not Morgoth would be at all interested in the ring. We read in the Silmarillion that much of his power had been diminished through selfishness and the domination and subjugation of lesser beings. If he were able to return from the Void before the destruction of the ring, perhaps he would be vulnerable to its allure.