Just to give the "other side of the coin" story. Twice in the last 3-4 years, I have been diverted away from ATL on an originating leg to HSV (my home airport). On both diverts, the planes did not pull up to a gate and we sat to wait out the storm. Despite my requesting over and over again, I flew onto ATL and then back to HSV.
Of course, as MSPeconomist notes, if you don't get to the 3-hour tarmac limit, they do not have to open the door.
So, it depends on the situation. You MIGHT be able to get off the plane . . .but, then again, you might get to fly it anyway.