Let me rephrase that reply a bit:

Most flights on the immediate days before Christmas, such as between 18-23 December, are fully booked. So, it's probably impossible to get on such a flight on short notice.

But flights on 24 and 25 December usually have a light load, so light that many of them are in fact cancelled. So, if you're late for check-in, chances are that you'll have to wait until the 24th or 25th to get available seats. If you're not willing to risk that, I'd not recommend taking such a risk.