The regulator isn't like a valve that shuts off. It regulates pressure by offering resistance to the flow from the fuel rail. It will hold pressure from the fuel rail for a time, but I'd imagine once the pressure from the pump goes off it just trickles through the regulator until it's equalized on both sides of the line.

'89 P'up, 2.6 I-Tec, 488,000 miles and done... gone to the great beyond