Can't see it. Rehnquist was already out of the Justice Department and on the Supreme Court several months before the Watergate break-in occurred. It's hard to imagine how he would have been in-the-know about a lot of the stuff Deep Throat supposedly revealed.
Rehnquist was the original prosecutor of the Ellsberg burglary...the break in prior to the Watergate wiretapping.
Ellsberg was the leaker of the Pentagon Papers.