neil,
If you are on a cPanel host and are contemplating moving to another cPanel host, I would say that there would only be a problem while the DNS update propagates (max 3 days but I’ve seen my website(s) updated in less than 15 minutes). cPanel has a great feature which would make the transition between hosts almost trivial.
HOWEVER, since you want to use Google Apps (and I know very little about their service), I’d bet that you would have to take the time to reconfigure EVERYTHING, i.e., this is NOT the solution you’re looking for.
Regards,
DK