If stoicism is a kind of proto-Cognitive-Behavioral-Therapy, and CBT improves depression, it really should. Gratitude is IMO very important to improve depression, and stoicism could help with that. Personally I must say that the negative visualization that Irvine proposes causes me problems rather than solve them, because it adds anxiety. Also, imagining things worse than what you have does not automatically make all things right - you can still long for a better version of your world while imagining a horror scenario.

Accepting reality as the only possible (and thus, best) reality works a lot better for me.

Identifying misalignments in my views of other people (or the world), which lead to negative knee-jerk emotions or general low-tune malaise, is another "mind hack" that works for me, but I would not necessarily call this stoic - but a CBT therapist might suggest that.

I wouldn't ignore physiological causes of depression, but on the other hand why not try? Who knows, maybe it will help you? A lot depend on what actually is going on in depressed person's life. There are different depressions, different people, and different cures for depression. In ancient times stoicism was recommended as remedy for melancholia. I'm subscribing to /r/stoicism on Reddit and this topic comes up sometimes, some people report that it helped them, e.g. https://www.reddit.com/r/Stoicism/comments/1kljc5/stoicism_a...