Boromir makes a good point of why he probably wouldn't have done in the first place, but as already stated even if he did inform him, there is no way a Nazgūl could do anything about it.
Proof?
The Nazgūl who flew over the camp on Dol Baran was not able do to anything. Now, indeed it did not directly respond to Pippin talking to Sauron through the palantir, the journey was too long and he had appeared immediately. He was actually sent to check on Saruman, but, even as its master detected Pippin and it was right above him it could not do anything about it.
So I doubt it could had done anything else sometime earlier.
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The invisible and the non-existent look very much alike.
Delos B. McKown
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