I would not. There is no imperative to upgrade him so long as the system is working. Just because MS drops support does not mean that the computer stops working or that crackers are going to start producing malware for his platform. In fact, right now, he is probably safer than many XP users. In this instance, security by obscurity DOES work. Nobody is going to develop a new virus for ME.
Hmmmm . . . good point. I tend to paranoid about viruses with him because he doesn't have a clue how to update virus software or even install MS patches, or how to identify e-mails that shouldn't be opened (fortunately, he also seems to be unable to remember how to open attachments or click on links). He did, however, manage to get a nasty virus a couple of years back, which required replacing his hard drive (fortunately all the data was salvageable, especially his beloved novel, which he can't seem to remember how to back up on a disk). I paid some techy outfit to take care of the whole thing, and they said they'd seen this unusual virus before -- it causes the hard drive to swing back and forth wildly and physically break itself!
A virus that affected ME would have to make it work better. There's no way it could be any more screwed up.