The only thing AADSAS obligates itself to is sending out your application within eight weeks after you pay the fee. Sometimes it takes the full eight weeks and sometimes it is faster than eight weeks. Supposedly, AADSAS will not hold up sending materials if all that is pending is a/a few LOR(s). However, you can have all of your materials at AADSAS and your transcripts verified and they might not send them for quite a bit of time after everything is at AADSAS. The friendly people at AADSAS make it sound like they send everything out in bunches or bundles. I'm not entirely convinced this is the case-it's just something they tell applicants to get them off the phone. The other thing is that schools can pull your information straight off of the AADSAS page before anything gets mailed to the schools.
Summary: AADSAS has eight weeks to mail your application. If you jerk AADSAS around they may very well take every minute of the eight weeks. Even if you don't jerk AADSAS around they still might take the full eight weeks.