As someone with clinical depression my whole life, I can answer this as no, the depression making me feel worthless is not connect in any way to my sense of "self." That's very seperate from any feeling in general, it just "is."

Sometime I get a feeling/swell of "wonderment" in response to my sense of self if I really concentrate on that "sense," but that feeling of wondermemt is just that: a response.

Also, anti depressants don't work the way most people think they do. In the cases of situational depression, they keep a person getting up and out of bed until they naturally start to feel better, in which case the meds are stopped. In cases of clinical depression though, it's more of a life-long medication that gets them out of bed in the morning. It dulls the depression, but it doesn't get rid of it.

All of that is disconnected from one's sense of "self."