I respectfully disagree with the above advice, you will not get any kind of penalty for submitting a FAFSA with their school code. It is best to get it done early. If you don't get pulled off of the waitlist until after the federal deadline to submit (June 30th I think) then you will get no federal loans and you will be ineligible for the grad plus loan. Furthermore IIRC some federal programs have limited funds, so they can be "first-come-first-serve." My advice is to submit it ASAP along with the other things that the above poster mentioned.
Schools will usually receive your FAFSA but they wont process it until you are accepted. You can enter multiple schools when you submit it as well.