Is it ever hinted in the texts that Sauron ever tried to acquire the elven rings of power and if so what would have happened if he did?
Sauron tried to acquire the Three during the War of the Elves and Sauron in the Second Age. After invading Eregion:
Concerning the Three Rings Sauron could learn nothing from Celebrimbor; and he had him put to death.
Still, Sauron guessed that Galadriel and/or Gil-galad were in possession of the Three, and so, after killing Celebrimbor:
Sauron's immediate purpose was to take Lindon, where he believed that he had most chance of seizing one, or more, of the Three Rings
(Quotes from the History of Galadriel and Celeborn, Unfinished Tales)
After the War of the Elves and Sauron, the Dark Lord seems to have been more concerned with men, and I can find no reference of another attempt to seize the Three. However, in The Quest of Erebor (Unfinished Tales) Gandalf says
I thought then, and I am sure now, that to attack Lorien and Rivendell ... was his original plan.
Moreover, in the Mirror of Galadriel (LotR I), concerning the location of the Ring of Adamant, Galadriel notes that
He [Sauron] suspects, but he does not know - not yet.
I can think of one other relvant quote regarding this, from The Shadow of the Past (LotR I):
The Three are hidden still. But that no longer troubles him. He only needs the One ...
The key point here (and hence my emphasis) is 'no longer'. I can't find a direct quote, but I think that Sauron ceases to be interested in seizing the Three once he realises that the One still exists. Had he obtained the One, the Elves would no longer be able to use the Three.
But all that has been wrought by those who wield the Three will turn to their undoing, and their minds and hearts will become revealed to Sauron if he regains the One.
(The Council of Elrond, LotR I)
This brings us to the final part of your question: what would have happened if Sauron did seize the Three? In the Council of Elrond, Elrond also says that the Three
... were not made as weapons of war or conquest: that is not their power.
Therefore it seems unlikely that Sauron was interested in the Three for his own use, rather he wanted to deprive the elves of them, either by seizing them directly or by obtaining the One. Either way, this would further his ultimate purpose: 'to cover all the lands in a second darkness'.
Yes Sauron did try to acquire them in the Second Age after he made the One. He attacked Eregion to get them and killed Feanor's grandson Celebrimbor. The Three had went into hiding before Sauron got there, but at this time Sauron's forces overwhelmed the Elves in Eriador and only with the help of the Dunedain was he driven back and nearly destroyed himself. See Appendix B in the Return of the King, and also Of Galadriel and Celeborn in Unfinished Tales.