To answer my own question, I think it does.
I think part of the attraction of post-apoc play is the tramping around in the destroyed bits of a civilization you recognize, even if only superficially.*
It has to come with some sense of what was before. Earth-set post-apoc has this. Games where science and magic blend together in a lost past (Tekumel, say) or there is just ancient tech (Traveller, notably) are more science-fantasy or science fiction with superscience than post-apoc. You can't mourn what you never felt you had.
In other words, it's not enough to just have the remnants of older civilizations around to explore, use, or play with. It's not enough to have old tech or old magic to be found in the ashes of destruction. The players need to feel some kind of loss for what's gone.
I think that's why Gamma World is effective. I think that's why Metamorphosis Alpha works (it's a ship, but it's a world gone bad based on a world you live in now). I think that's why T2K works. You can't go home again because home - all of it - is wrecked. But you can try to build something new out of it. There isn't some great shining beacon to retire to, but you can try to build one.
To me, no sense of loss = no post-apoc feeling. Just science fiction or fantasy or science fantasy.
* This is why 25th century Gamma World has STOP signs and revolvers and "No Nukes!" shirts in the art.