Yes. It's one of the biggest vectors for contagions. But since disease takes a while to become evident, most people don't associate their sickness with the actual source of transmission.
Bathroom doors specifically, not just doors in general? Edit: I looked it up and I guess it's about bacteria like E. Coli, that makes sense. It's weird, because people on Reddit/Lemmy always talk about using these tricks to avoid touching things, but IRL I've never seen anyone do it or heard anynone talk about it