Once you submit your application through AACPMAS it will take a few days for it to be verified, after which the schools will receive your MCAT and transcripts and whatever else was on the application. For me it only took a couple days after that to start receiving interview invitations.
AFAIK it doesn't matter if you send in your LORs before or after, the admissions people I talked to said they create a file for you once you send in your first materials (application or LOR or whatever). I sent in my application first, but that was only because I didn't have my letters ready at the time.
Hope this clears it up a little, I was wondering the same stuff when I applied last month.