Grrr. If you end up "eating" those session bills, you can ask your T to only charge you the insurance rate at least. (The amount T would have collected from insurance, not full rate.)
Dysthymic Disorder, while miserable, is not a biggie "secret" to worry about. IMO. People at insurance companies don't really care what each person has or doesn't have in the way of disorders...they are "just" paper pushers and have their own lives.
Rest assured that dealing with insurance companies will be part of your job... assuming that you are approved by them to offer coverage, and that you are affluent enough to afford them! (Talking about you being on the "other side of the desk.") Sure is time to think about that one