I've pondered the question of which causes what for years. Did depression cause my alcoholism or the other way around. Ultimately, I think your question, 'does it matter is rhetorical. No it doesn't.
I'm an alcoholic who also happens to suffer from depression. Wasting energy, time and emotion over the cause ultimately got me nowhere.
I'm going to focus on my sobriety and hopefully the depression will lift. If it doesn't, ce la vie. They are mutually exclusive events in my life.