It sure would. Not to mention making it easier for the starter to turn the engine over if all the bearings were flooded beforehand.
It's SOP for large marine diesel engines and it's found on some aircraft, but I specified it on auxiliary and emergency generator sets that sit for days and weeks at a time with their heaters going. I know that it dries out the bearings and when they start up, they are required to almost instantly provide full power.
That's gotta be hard on dry bearings.
Sigh... Yep, and It could be sooo simple like the glow plug light on old Mercedes diesels. When the light goes off, the oil pressure is at, say 70%. When you start the engine and the pressure builds up from the mech pump, the aux pump shuts off. You could have six figure odometers like the old MB oil burners too.