it stops processing the current file and switches to that one, and doesn't return until that one is totally complete

Yes. Functions and files are executed from top to bottom. Unless you make it not execute from top to bottom.

(as in not just the BEGIN blocks of the second file)

Right.

And if it hits a use of a module it is already in the middle of processing, all it will do is call that modules import sub, and not try to compile it's code a second time (thus preventing loops).

Not quite. Being "in the middle processing" has nothing to do with it. require and thus use do not execute a file it that has already been executed by require, use or do, or more specifically in %INC.