Can you actually hatch a Pichu with the Ash hat?

YES, you can.

I hatched one this morning from a 2k egg, which I believe I got yesterday (i.e. after the "event" began). I've taken a screenshot, with the pichu at an angle for authenticity. ;)

I didn't realize it was possible, as the previous two hatted pikachus came before the baby pokemon were added.

Not sure if you have a definite chance of getting one with a hat or not, unfortunately.

Not sure if it's guaranteed, but the first two 2km eggs I've hatched since the event started (and picked up since then too) were Ash Hat Pichu's.