So I tested whether a Melodyne Region FX on a clip was copied or not. It varies:
Clone track does (as one might expect)
Drag copy does also (somewhat unexpected, but nice!)
Copy/Paste Special doesn't, although a Melodyne Region FX appears on the clip!
All very confusing really...
It leaves me with the feeling that Copy/Paste Special is a bit broken, which is a shame because it would be the quickest way to copy a track from one project to another. The best way at the moment seems to be to use a track template to copy the track info, then simply copy/paste the clips.