Gandalf believed Sauron did not immediately learn of the fall of Isengard.
In the books, after Pippin looked into the Palantir which Grima Wormtongue had thrown down from Orthanc, Gandalf surmised that Sauron believed Pippin had been taken prisoner by Saruman and made to look into the Palantir as an act of cruelty.
From this, we can guess that Sauron was unable, or unwilling, to simply look through his own Palantir and see what had happened to Isengard.
The question was not explicitly raised again -- the main characters were focused on more urgent matters, just as Sauron was. (Edit: This is incorrect, as noted in other answers -- it was discussed, and Sauron sent a Nazgul to Isengard to investigate.)
However, it was not in Sauron's nature to trust Saruman. He almost certainly had spies in Isengard. One of these would eventually report back. It might only take a day or two if the agent had a fast way of sending messages (through birds like Saruman's crows, or by making contact with one of the Nazgul). On the other hand, travelling overland from Isengard to Mordor would have taken some weeks, especially since the agent would have to be wary of patrols from Rohan or Gondor.
So Sauron probably learned of the fall of Isengard before the destruction of the Ring, but it is plausible that word might not have reached him in time.