I've been at the meetings where they discuss the drop in classes. I've taken two drop in clases myself.
My impression is that being closed out is very rare. (maybe even a totally theoretical possibility.)
If you show up early -or even on time - you might have to wait outside for F.R. staff with a key to arrive. That happens maybe 1/3 of the time when I volunteer there.
I could be wrong, though. You might want to arrive 5 or 10 mintues early and have a book or a harmonica to amuse yourself with.