I'm guessing that would depend on the type of culture: the whole thing would be a blob of medium rather than an even layer, so the cells could only attach where the blob touches the dish. Since most culture dishes are coated, I'd say if there is contact (and not just transient, but static enough for cells to attach), they will attach under zero-gravity conditions as well.
@Erik Haefner, sounds reasonable. And I think this question is very intriguing. I wonder if the adherent cells stick on the dish depending on gravity. Or the morphology of cells will keep the same?