In KOTH mode, does the counter increase faster when there are more people of the owning team on the point?

No.

The number of people on the point matters when capturing it (capped at 3 people for maximum cap speed), but once you own the point, the percentage meter fills up at a static rate regardless of team presence.

I have video proof that I can't upload currently. Before I do, I'll probably edit them together to give a side by side view.

From my oberservation i can say that you don´t have to stay on the point after you captured it.

I had a round in Illios where we captured the point and drove our Enemies back to their spawnpoint and won the round without any of us on it.