Having never been in the military, I'm not in a position to address the issue personally, however,
I enlisted fifteen years before there was such a thing as a diganosis so I cannot speak on if somone is medically eligeable. I was still on active duty for another seven years after my diagnosis (you can stay on active duty with some disabilities that were incurred in service) and the therapy and training I got has made a complete difference in my life. I left the service much more functional than I entered it.
As far as the environment goes I found it to be comfortably regimented. I always knew what the rules were, what I was supposed to wear, where I was supposed to be, what I was supposed to say to someone. As an Army truckdriver I was mostly left alone in my truck and no one thought it was odd or reclusive because well there was only one driver per truck and you drove all day nothing odd there, right?
I did two combat tours and innumerable field exercises. It's loud, bright, smells bad, chaotic, high pressure and unpredictable. Someone will give you one set of instructions and their counterpart may give you a different set. Then you get yelled at when you don't get them both done at the same time. Unlike most of your peers you will likely not have the easy cameraderie to share your feelings or a good working understanding of the friendly horseplay and such the others engage in to blow off steam. This may make the environment more difficult for you. Eventually (usually within about 3-4 years) you will have to be in charge and tell others what to do and explain to your supervisors what you have done and why. You know your abilities better than I do.
Ultimately you need to remember that people's lives are depending on your ability to do what you are there to do without freezing up or falling apart. Judge yourself honestly and it may be the best decision you ever make.