OF COURSE THEY DID! Janeway really did need a break and lying about on grassy knolls talking poetry wasn't gonna cut it.
Plus if there was a problem with him being her underling he could just activate the Emergency Command Hologram and don some red undies when they were doing it.
If they were "doing it" then why would he have underwear on? From what I know, certain body parts have to be exposed during the act.
Well okay the whole dude was in Red command as soon as they were ready to liaise. The underwear, that's just my special touch. I'm a romantic.