Alot of stationary military equipment is run this way. The hot to the fuel pump or diesel fuel cutoff solenoid relay is run from a oil pressure switch. In the case of military stuff you crank it until it builds oil pressure and then let the key go. If you let off the starter too soon it just dies. It sounds funny too, like your starting a car thats already running but it works. The downside to it is that the military equipment that had this was stationary so if it shut off it was just a pita. I would hate to think what it would be like on the highway and your a quart low and it shuts the truck off. For trucks and things they had a low oil buzzer so if you could find 2 different pressure value switches to buzzer first and shut off second it might be a idea.
Having the bypass switch would be nice. On the military stuff we called it a battle short switch. In case the sensor got fubared it would still run.
Hope this helped,
Morgan