In working with the disabilities offices at several schools, having a disability on file and working with the office is designed to help provide accommodations (notetakers, recordings, extended time on tests or for projects done in a class period, etc.) to help you do the work on time. The timing of when things are due is up to the professors; they can grant exceptions but do not have to. If you need extended time to take a test or to do a project in a class period, the time can be covered/accommodated for the disability but they still have to be done before or on the due date. Your school may be different, contact the disabilities office to find out the school policies to get help or know where you stand. Otherwise it has been my experience that it is up to the professor if the due date is extended.