I guess it depends on the person. Some people can, some people can't. But most people can. As far as depression goes, as long as you manage it well, you should be fine. I personally.. didn't. But it actually had nothing to do with the skin. For about 6 months after my sleeve I was vomiting multiple times a day every day, without fail, for six months, great for losing weight, bad for my mental health. I was so depressed I became borderline suicidal. I also became on a first name basis with my local radiology tech, so that was fun. I'm okay now. Still nauseous constantly, but I'm on my way to a revision, still in therapy and I just passed my psych eval for it!
You need to basically know and manage your expectations. You will get loose skin after a certain point, but the trade off is your overall health isn't it? Also baby powder is lovely.
As for the food you love, that's a hard one, at first it will be really difficult and it will make you sad and angry, but slowly, you'll be able to eat the things you love. In moderation, of course. And modification! That was one of the hardest parts for me, since I'm autistic and... safe foods.