Can a Pichu wearing a Santa hat hatch from an egg?

As described in Why is Pikachu wearing a Santa hat and what does it mean?, there is a limited time promotion where wild Pikachu can be wearing a Santa hat. Additionally, if they are evolved into Raichu, they too will be wearing a Santa hat.

Pikachu's pre-evolution is Pichu, and the most recent update announced a Johto Holiday and the ability for Pichu to hatch from eggs

Professor Willow has discovered Togepi and Pichu hatching from Eggs! Starting later today, Trainers will have the opportunity to hatch these and several other Pokémon that were originally discovered in the Johto Region in Pokémon Gold and Pokémon Silver video games. These are the first of more Pokémon coming to Pokémon GO over the next few months.

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.