If the pump stops running, the oil flow would stop, and I suppose the shaft oil would vaporize. Perhaps, the vapor would bubble up, and liquid oil would take it's place to some extent until it formed a sludgy goo that slowed the shaft to a stop. I presume the shaft would eventually seize, but hopefully, this wouldn't be a catastrophic problem for anything but the turbo itself.
Is this loony, or could it work?
Were you betting on loony? You need pressurized oil on the turbo bearings. The shaft will sieze VERY fast if there isn't oil pressure. In fact cars often have turbo trouble when the owners shut the engine off right after a high pressure run. The "coasting" turbo can cause bearing damage.
Bill Jepson