I'll ask specifically about the stairs, but doubt I'll be allowed. The good news, at least, is that the bike rack is in front of a big window and the building's deli. I don't know how much deterrent that will provide, but it's better than none.
So, just attach the lock to the bike rack, and leave it there overnight. I like it.

Anybody ever come back the next day and find their lock has been "removed" by maintenance? I guess that'd be a sign that the lock wasn't worth the money ... I don't want to wear out my welcome doing this, but I want to carry a bunch of bike locks even less.
Thanks for the tip. I'm going to try it, and probably be very happy not having to carry the locks around.