Yes, most schools will offer you their supplemental before your AADSAS app is officially verified.
After submitting your application on AADSAS, most schools will e-mail you an invitation to complete their supplemental application within a few days.
Some schools will do a preliminary review within a couple of weeks after you submit, decide if you meet their minimum requirements, and then send you a supplemental application (Midwestern to name one).
You can expect to get right back onto the supplemental statement grind within a day or two after submitting, depending on the specific schools you're applying to and whether or not they require supplemental applications.
