It depends. I managed to work at 4 different locations on my CP. And no... they were not always closing. Although they were most of the time but that was because they asked us what we would prefer. (Could be my GSMs though...because I also got atleast 2 parades a week)
Anyway. It all comes down to what you have to offer and how motivated you are to do things.
I started out in Ops for one ride then I got hurt on my 2nd day of training and they changed me. That was still in the same land (MK). Then, since I spoke many languages I ended up doing a lot for guest relations and working there too (especially with the brazilian tour groups). I also worked entertainment.
Also, I am not an exception. One of my friends started out in transportation for her CP and ended up in Human resources (and to those who say that you can only do that for medical reasons are wrong...she was not hurt)
My other friend started out in AK and then ended up working in film production.
Just always keep your eyes open for opportunities. Get along with your GSMs. Be excited and make your own opportunities.

And if you are unable to switch or be co-oped out, don't worry and just make the most of your time there. If you keep your status as a CM you can request a change later.