[Occasionally6]

It will work if you keep the inlet pressure to the fuel rail higher than the bleed off pressure at the regulator. That way the fuel pressure is still set by the fuel pressure regulator rather than the pump output. The only change is that less fuel is required to be bled back to the tank in order to maintain the lower pressure in the rail.

There's not all that much to be gained though. A fuel pump might draw 7 amps at 14V so just under 100W.

You might try to use the pump input power to control the fuel pressure without using the mechanical regulator but the relationship between pump input power and fuel pressure is non-linear. That means it would be necessary to map the input power to pump output vs manifold pressure. It's a lot easier not to have to do that, leave the mechanical regulation in place, and accept that the pump will run a bit harder than strictly necessary.