I'll say no. The strong impression I have of the Ainulindale is that Melkors dark thoughts were largely the product of his time in the Void, that while he was in the presence of Eru he was, not dominated, but influenced by his maker, and preserved from the kind of active evil we see in him on his return from the Void. In the Void he encounters Not-Eru, the absence of that wholesome positive presence preserving him from predation by baser urges. If Eru is defined as positive and good then, by definition to encounter his absence is to encounter the negative and evil, and it is then Morgoth becomes infected. It was not a destructive urge that sent him questing for the Flame Imperishable, after all. So, if the question is could some other of the Ainur, or even one of the Maiar, have made the same trip and fallen into the same trap, sure, though in the latter case it would have been a miserable rebellion, confronting the combined power of Eru and the Valar in the Ainulindale then the Valar in Ea, a combined might that would include Manwe AND Melkor in concert. If, however, the question is could one of Eas inhabitants have fallen after the Ainur entered into it and began to shape it, no, I don't think so; I don't think it possible for the Maiar and extremely unlikely for the Valar because it requires a trip to the Void of which I don't think the former still capable or to which the latter remain susceptible.