From what we know the last day to turn in drops is 12/20 at 11:59pm (even though the vendor is usually up until server down in the past). That usually coincides with when the mobs stop spawning too but they might end the mob at server up on the 20th so technically that day would only be for turning stuff in.
In the past I always wrapped up a day or 2 early with the ToT event so that I wasn't stuck with unwanted drops or unclaimed rewards; I'd rather be safe than sorry.
All that said, only a Dev can give a definitive answer on this.
Comments
As said above it usually really ends at the next server up. But if you are doing it after, don't log out or you can't use the NPC.