Not sure that would be particularly effective - it sounds like many of those there were Downing Street staffers, most/all of which will have been working that day.
Additionally, any of the other comings-and-goings could be for legitimate work, meetings etc.
It'a also possible any of those who were in Number 10 were working and didn't attend the party - reports suggest that Johnson was one of them, other than briefly saying a few "Merry Christmas and thanks for all your work" type words.
It might need someone to whistleblow. Shame Dirty Dom had already jumped ship at that point...
I'm sure the Cabinet Secretary and Head of the Home Civil Service will get to the bottom of it.