Actually, database connections would happen only on the first pageload per apache server spawned. Apache::Session sits on top of DBI, and database connections are cached (as any global variables are) if you use mod_perl. If you use Session on MySql your sessions are still going to be very fast, and any performance difference from memory-only sessions would in most cases be offset by the object persistance advantage you get with Apache::Session (otherwise you'd usually need to fill in the session data yourself, with the accompanying db quieries).

I recommend you look at the mod_perl documentation for more on how DB connections are cached.