Seeking asylum? Sorry we are racist...

[Jurion]

Well, you must take in to account the fact that the Valar were no longer the rulers of Middle Earth in the Third Age, they gave up their rulership after the Numenoreans tried to invade Aman.

Then Manwe upon the Mountain called upon Illuvatar, and for that time the Valar laid down their government of Arda.

From Akkalabeth, Silmarillion

But still the Valar would have most likely sent an army if Sauron had conquered Middle Earth, just like they had sent the Istari, but they would not have come themselves. They would probably have sent an army of Elves as was suggested above.