Pumping no oil or dirty either way is going to cost you the crank, mine marred the crank and required it to be turned and oversized bearing which was $20 less than a new cast crank. So if you have a $500+ crank in it do you want to risk pumping dirty oil to the bearings and see how it plays out?
ZERO oil pressure is gong to do a heluva lot of damage to the engine... end of story. This is why the wrenchies at GM etc put a bypass into the oil filter systems to keep oil flowing no matter what.
"Dirty oil" is a relative thing. The motor oil in the pan is either clean and new or it has some miles on it collected while being pushed through 25-30 micron filter paper. Sooo... The "dirty oil" is not going to have anything significantly larger than maybe 32 microns in it. If 32 microns for a few seconds is going to badly damage your rod and main journals you have a poorly manufactured crank with improper Iron alloy that won't heat treat at all or poor heat treat process performed on the journals.
If you have so much really big crap in the oil that it's going to seriously damage the crank in the few seconds the 25-30 micron filter is bypassing at 0°F you didn't properly clean the engine out after the machine shop worked on it. I always rod out those oil galleries with brushes and douche out the block several times with Kerosene or Diesel before assembly. I also douche out the oil cooler using Kero and compressed air or just plain replace it. I've seen several engines in impatient buddies rigs that were completely destroyed by sand or iron filings leftover by the machining operations... even after a round or two in a hot caustic jet spray machine... or crud in the oil cooler that they didn't flush out. The oil filter will not keep you safe from that stupidity.
Typically the filter only bypasses at startup when it's cold as hell or you are running oil that's way too heavy for the temps. Either way it stops bypassing pretty quickly after startup and as noted above the particle sizes will be small enough that they will pass through the filter anyway.
This is all I have to say about it.