I started swimming while I was in the depth of depression (induced by external factors) and yes it did help manage the depression, but didnt solve it. What solved it was leaving my alcoholic ex and getting control back over my life.

I have continued swimming and I also do a lot of cycling as well as some hiking/tramping and the ocassional bit of mountain climbing, and they do help with managing stress and mental health but they are no longer the primary reason I do them. The health benefits I get from exercise are mostly physical but those benefits also play into making me feel better about life too.