I do not believe that a mission necessarily makes you feel "accepted" with Heavenly Father if you didn't feel it was right to go in your situation, and I've never liked the part of the LDS community that is so focused on whether Joe went on a mission or not.
I do believe that when you don't get answers, it's often Heavenly Father saying it's your decision and you need to use your intelligence and feelings.
That being said, going on a mission with depression is a very difficult thing that can make it hard to serve. My question is... how controllable is your depression? Is it fairly debilitating at times, or can you manage with it and to what extent?
Now do you want to go because it will mean being accepted? If you want to go because you think God would like you to go, I think that's a decent reason. If it's to please people, that's not. Personally, if someone told me they couldn't serve because of a condition like depression, I wouldn't think twice about it.