LOL, oh yes, you are going to fit in beautifully here. >:D

Fantastic! Yes, I don't see why that would be a problem. I assume McCoy will need to get some bed rest after Bashir sees to him, so you could likely have it so any tag-ins are timed after the thread with Bashir, when McCoy is resting and recovering. Conversely, you could also have McCoy appear in Ten Forward first to cause the biggest hubbub, and later have him moved to sickbay. We're pretty laid back here, so feel free to play with different options! :)