I have dropped off/picked up passengers at Red Hook. I also use Kevin Campbell which makes all work even better.
I will get fuel(top off) and drop off passengers... with significant fuel purchase and drop off not taking any additional time, I am still charged drop off sometimes (and sometimes not, since it is occupying dock only for fuel purchase).

If I am also picking up passengers, I will drop anchor and await call from Kevin that they are on the way from airport, at which time, I raise anchor and return to T-dock for pickup (And pay fee).

Would be nice to stay on T-dock or slip and if needed, resupply provisions from grocery store across the street.