I think you should make a very clear distinction between tragedy and futility. Classically literature has recognized both tragedy and comedy as essentially heroic forms. In a tragedy, the hero strives for a goal only to be overcome by opposing forces, or by their own fatal flaw, but still they strive, they follow the heroic path, they try.
If there is "comic relief" in a tragedy, it is not really to lighten the mood. It is more of a counterpart, a form of irony. It is also very human. We do laugh in the face of danger and despair. As my mother's family liked to say, "you have to laugh or you'd cry." But the reader does not really need relief in a true tragedy because there is still a heroic arc. Even the tragic hero, the doomed hero, strives as if there were hope, and there is a moral dignity in that that draws us in.
The post moderns, however, indulge in something quite different: futility. The do not believe in the heroic hope, in the moral dignity of tragedy. For them life is simply futile, and so they write stories of futility, of unrelenting bleakness and cynicism. Can there be comic relief in such a story? I'm not sure. What would there be to laugh at? If there were comic elements, presumably they would be a comedy as cynical as the despair that drives the whole story. It might be comic, but would it provide relief?
Which of these, tragedy and futility, is depressive? Both, perhaps, but in very different ways. In a tragedy we are depressed because hope was not fulfilled in a particular story arc. But this is not a denial of hope. It speaks to its uncertainty, not to it futility. One may come out of tragedy with hope, even with joy, and certainly with an affirmation of the dignity of the human spirit. But with futility there is none of this. Futility is inherently and fundamentally and comprehensively depressing. It discovers no hope, no dignity, no affirmation of anything except futility.
The depression of tragedy is relieved by its positive affirmations. The depression of futility is only confirmed by it lack of affirmations. Comedy, I think, can only corroborate the general effect of these two genres.