Like everyone has said, yes, some people will leave because of it because they aren't equipped to handle it. However, the RIGHT person won't leave because of it, they will want to stay by your side and help you.

My advice is to have lots of information available to your boyfriend. Some people know nothing about mental illness/depression while others are very educated. If he is the type that doesn't know much about it, it may scare him - the more factual information you can provide him, the more comfortable he will be with it. Also, make sure he knows you're not expecting HIM to fix you. Let him know what you will do to help yourself - go see a doctor, take meds, get a therapist, etc. Think about what role you want him to play in your depression and be honest with him about it (whether you just want his support or whether you want him to be more active in your therapy and things like that, etc).

My ex-husband was very patient and understanding, he learned a lot and was there for me. My current boyfriend doesn't really understand anything about depression but he's still very supportive. He just needs me to be more direct about things (like if I want to talk and just have him listen, I have to tell him that's what I want, etc) whereas my ex-husband instinctually seemed to know more of what I needed/wanted.

Good luck - for me, I personally think it's very relieving to open up to someone close to you about what's going on.