Yes, it is possible to be too depressed to actively participate in therapy. This happened to me the first time I went to therapy as an adult. I could do nothing....not even talk.

In this case, the therapist needs to be doing "supportative therapy" in which they boost your ego, while you (a) get improvement through medication, and (b) get a stronger ego through their connection.

It does not mean the therapist should abandon you. It just requires a different approach to the therapy.

Good luck