Sure, there is certainly a chance you two could get back together. Nothing is impossible. Yes, maybe the situation hurt her, but this is a case where you did not do anything intentionally or maliciously. It would maybe be different if you were some kind of complete jerk, some kind of abusive a-hole who was just oblivious to the fact that he was an a-hole. That wasn't the case here. You didn't do anything with malice or intent. You were suffering through a terrible depression. Now, that's not saying she did anything wrong either, per se. She tried to be with you, but she just hit a point where it hurt her too much. So, she did do the right thing for her.
I think the important distinction here is that it was more the situation that hurt her than it was you. She cared for you, but she saw that (at least at the time) you didn't seem to care for yourself. What's worse, that made the relationship suffer. She left because it hurt her too much to see things deteriorate so badly, both for you personally and for you two as a couple.... and for you seemingly to do nothing to change that. Don't misunderstand my words. I'm not saying you did that intentionally. I've dealt with depression enough myself to know it isn't a choice. But, it got to be too much for her and she needed to leave for her own well-being.
....The thing is, now you finally HAVE started to fight for yourself. You finally HAVE started to fight to get better. So, if you give her time, it is possible she could see that you've begun to fight for yourself and she may feel that you could be worth another chance. For now, though, just give her some time. You've tried contacting her a few times and she's asked you to stop. She's asked for her space, so give her that for a little while.
Hopefully she reaches back out to you in time. If she does not, though, after waiting a reasonable amount of time (whatever that means to you), try one last time to ask her just to give you that chance. If she is still unwilling, then it would be best to move on.
Sure, there is the chance she could be willing to give you another chance..... But there's also a chance that she won't be able to forget what happened before. Even though it wasn't your fault... it wasn't like you intentionally gave up on the relationship.... it may still be too hard for her to no longer associate you with the feelings she had when things were at the worst. So, that is a possibility you should at least prepare yourself for so you are not blind-sided by it.
I hope things work out and she does give you another chance. That is what you want, so that is what I would wish for you. But, please know that is so much more important that you continue to fight for your own happiness, even if that does have to wind up being without her. Nobody deserves to go through what you did, so please don't give up on you. I know from experience that depression can be a life long struggle.... but it is a fight worth fighting, because the alternative is definitely not good.
Good luck to you.