Hi Jana,
Many people who take the At-home version of the GMAT receive their Scores within 2-3 days. However, a certain percentage wait upwards of a week (and in some cases, far longer than that). Unfortunately, there's no way to predict how long YOU might have to wait if you take the the At-home GMAT during the last week of December.
Many Schools are actually 'flexible' when it comes to accessing your Official Score Report - as long as the rest of your application is in on time. It often takes weeks (and sometimes months) for Business Schools to decide who to invite to School - so if you are facing an upcoming application deadline, as long as your Official Score will become available sometime in the near-term, then you might be fine applying as is. If you know the specific Schools that you plan to apply to, then you can reach out directly and ask about this issue (the Admissions Department at most Schools would be happy to answer any questions that you might have about applying).
GMAT assassins aren't born, they're made,
Rich