Can a Pichu wearing a Santa hat hatch from an egg?
Just hatched a pichu with a hat. So while they may not have had hats during the 2016 Christmas season, they do during the 2017 Christmas season.
As of this Christmas season, Pichus can be hatched with the Santa hat. See this answer for proof.
Based on the post here, it looks like Pichu are not hatched with hats, since Pichu and other babies went live at the same time as the Santa hat Pikachu.
I've hatched two Pichus and one had 91% perfect IVs so I evolved it. The resulting Pikachu does not have a hat but I've caught a bunch of Pikachus with hats and got the eggs after that was live.