Engine pre run oil pump

Well, if the majority of engine wear occurs at startup, why not....
IMHO, an arguable assumption.... If you look into this start-up wear matter, most of it is due to bore and ring wear due to rich start-up mixtures (especially with carbs) and pistons loose in the bores when cold, so pre-oiling does little to nothing for that. And it does not necessarily put any oil on lifters and cam lobes.

It ought not hurt anything...... unless something blows out in this extra system's plumbing and wrecks the engine from loss of oil. So you might want to weigh the odds of that versus any perceived benefit.

BTW, the Accusump solution has been around for 4-5 decades.