My dear, your question is a little confusing... because it sounds like to me that he is taking the first step to either leaving or just wanting some space of his own to have some independence. Depending on how old you both are and what type of depression he 'had' he just might need some time to himself to work on why he was depressed and how his recovery is progressing without your interferance. So, IMO, the question should have been whether you should let him go if he wants to leave..
Do you know why he was depressed? Did you have something to do with helping him 'get better'? Or do you feer that he was with you during this time and used you as a crutch?
As far as your snooping - this shows distrust and if you do not trust him, then you are not secure in this relationship either. As humans, we learn and grow and develop as we get older and go through a lot of changes - with or without our partners. And, we should never place anyone else in the center of our universe - that will only hinder growth. If you really care for someone, you help them in their growth while you grow also and accept each other's changes. Apparently, you somehow don't accept his change or you would not have thought of snooping and that's insecurity on your part. I hope you can learn to accept and adjust to your changes as well as his and don't push him away. If he still cares for you and your relationship, he will continue with you even if he has his own room, and there is really nothing you can do to make him give it up. It is his choice and you should respect that.
If he leaves you for good, it will be a lesson learned and you need to accept that and go on with your life as well. There is no guarantee that all will work out well, we can only hope we did the right thing and go on.
No matter how this turns out, respect yourself and get rid of the snooping urges, they will only make things worse. We will be here with you to help you cope either way, so keep us posted.
Good luck.
http://smileys.smileycentral.com/cat/15/15_11_2.gifCommunication and trust are keys to any relationship.