I have a hard to spot physical illness rather than a mental one, so my situation is slightly different. It has caused me to be absent from college a couple of times, although I have never missed a deadline due to it. However my recommendation is too not disclose on your application, as you mentioned it just leaves you open to be discriminated against regardless of what the law says (this is more of an issue with job applications but it still holds true for unis). However DO disclose it in private to your lecturers if it does cause you to miss class, I have found my lecturers to be sympathetic to myself and others in my class provided there excuse is valid and not overused.
The only time I ever disclose my long term illness is for insurance purposes during my last two jobs (which involved driving, my illness is DVLA recognised so I MUST disclose that I have a license restriction), otherwise I find it wise to just keep your own medical history between yourself and your doctor. It is your human right to have a private life so you are not doing anything wrong by non-disclosure.
Although disclaimer, again especially in work places, if you do not disclose you do not recieve any of the benefits outlined in the Disabilities Act. Meaning you will not be able to use your illness as an excuse in a legal setting (employment tribunal) or to an examination appeals board (no extra time for exams).