No, he doesn't.
Listed below are the episodes where Q is present (and his presence is known to anyone on the ship, as we can assume that Q always watches the Enterprise ;) ) and whether any reference to an admiral (on-board) appears in the scripts:
- [TNG] Encounter at Farpoint - Admiral McCoy leaves the Enterprise before Q appears, so NO.
- [TNG] Hide and Q - the only admiral onboard is Q himself (pretending to be), so I guess it does not count, therefore: NO.
- [TNG] Q Who - NO
- [TNG] Deja Q - NO
- [TNG] Qpid - NO
- [TNG] True Q - NO
- [TNG] Tapestry - NO
- [TNG] All Good Things... - Admiral Riker's case excluded, therefore: NO
- [DS9] Q-less - NO
- [VOY] Death Wish - NO
- [VOY] The Q and the Grey - NO
- [VOY] Q2 - NO
As far as I remember, in DS9 admirals do not arrive at the station before the Dominion War or its prelude, and in VOY, there are no (real) admirals on board during most of the episodes.
Therefore, the answer to the question is that Q does not appear aboard USS Enterprise, USS Voyager or Deep Space 9, during any admiral's known stay.