I don't see how it would matter. I can reduce the pressure to zero with the pump running. If I had the my Bianca plumbed; I'd be able to lift the levett halfway and get line pressure, and needle valve control that from say 3 bar, or whatever the limee pressure is, down to zero. If you turn the pump on, it would be the same as with the tank model.
Even without a needle valve, a plumbed E61, or any other plumbed machine with the proper switch installed, can do a long line pressure preinfusion for as you please. That may capture a good proportion of the profiling benefit, since it would permit super fine grind shots.