Can yoga really help someone who's depressed?

Physical activity is good, plus getting out of the house and being among people should be helpful as well. Get another perspective on life that isn't just your own thoughts. Sunlight may also help, and getting out can get you that (although not today where I live; it's pouring here).

Certainly it isn't anything that can possibly hurt you.

Talk with your doctor to make absolutely sure and also to give him or her a heads up about this. It's probably fine, but you can never be too careful.

And I'm really sorry this is happening.

Absolutely. Exercise in general has a huge impact on mental health, and mindfulness, deep breathing etc does too. I don't personally have any experience with Yoga but my understanding is that it combines a lot of both sides of that.

But if yoga isn't your thing just practicing deep breathing/mindfulness and getting some good exercise will be just as good if not better. Don't let any doubts or the learning curve on yoga hold you back, go for a 20 minute run and you can see for yourself how much better you feel. Do that every day and it will absolutely make a huge difference.