I'm assuming since the dev blogs have said he's not supposed to be able to equip armor, and other armor, including hats that look almost identical to the lucky skullcap have given a 'unfortunately you can't wear this' message when I picked them up, that this is probably not supposed to be the case.
It also did not render on his model (not really surprising, I'm not sure how it'd fit XP), which further suggests it's probably not supposed to be doable.
I have a screenshot if its needed but it's on my other computer so I don't have it right at this moment.