I really have no idea, but I would guess that they do have access to the schools you have applied to. AADSAS says that schools have complete access to your complete AADSAS application...part of which shows which school you applied to and what your status is. I really have no idea though so I would wait until the next person posts...maybe they know!!
In Texas they know quite a bit. Residents of the state do not use AADSAS, but rather TMDSAS. From what I was told (at Houston), all Texas schools know not only which schools have accepted you, but also which schools you've sent your deposits to. Thus, schools are very much aware if someone is playing games and holding more than one spot for a long period of time.
As far as AADSAS is concerned, I have no idea the type of information that schools share.
what i've heard from the ADCOM members is that they don't know how many schools you applied to, but they do know if you've accepted school offers on admissions, the schools share that information with each other, and so those that have accepted admission to a couple of schools might be less off in receiving admissions than those that have no acceptances. at least this what i was told by a member of a UW's ADCOM.