Yes, and he comes to visit your tama on Cristmas eve. At 11 pm or 12 am (I'm not 100% sure of which one because people have reported on getting visits from the Santa at both times).
I think you must change the date to Chrismas Eve and the time to 10:29pm and wait one minute- though you do NOT get to keep the present he leaves, it's only an animation........... h34r: