I do think doing a bit of movement even if just getting yourself from the bed to the door is probably going to have a bit of an advantage
I don't think so. Not for the recovery from the illness. An acquaintance suffers from severe ME and trying to exercise despite it worsened her illness horribly.
Of course, in general, moving a bit is a good thing, as muscles atrophy, etc, if you don't, but from what I know about the cause of ME, I do not see how exercise should help at all, but I do know it is massively harmful.
A person whose ME has been healed (not sure if there's any proven cases, there doesn't seem to be a real treatment offered) would profit from increasing exercise to regain muscles, etc.
But first the illness must be treated, and there is no way exercise could help. Someone with some unspecific kind of "CFS" perhaps, but if you know it is ME ... no.