That's a new theory, a very modern-English-centred one (and therefore anachronistic; it's actually from the Islamic world, 11th or 12th century).
That's not the origin of counting sheep (the association went the other way). So pandas
could work (if counting sheep ever does work), since the cuteness-overload might fulfil the requirements.
@Cynn
This chapter did make me look that up for some peace-of-mind, and, yeah, the actual number is unconfirmed. There are various estimates, but which populations they count drastically changes the numbers (the subspecies and those in captivity may or may not be included, for one). That's actually closer to the estimated number of red pandas (that's just as sad, or worse). But they all do better in the wild, so… Sleep well.