I think they may only have 12 or so ride vehicles for Twilight, so Potter VR should be 12 times as much capacity, theoretically, 12 x 240 is 2,880 per hour, but that's assuming similar ride length and load times as Twilight.
According to rumors, there would be 6 preshow rooms where groups of 24 would enter. In addition to learning story details, this is also where guests would be fitted for the headset part (minus the heavy VR elements). That would save time in the actual broomstick rooms, which would be smaller and only contain 6 seats each.
Things could of course change from the Epic concept to the Studios version.