On all the vehicles I've owned that have actual oil pressure gauges, the oil pressure on cold start-up and at idle was pretty far below what the oil pump pressure relief was set to. Now if you revved the engine up pretty high right after a very cold start-up then you could get the oil pump to hit pressure relief.True, but oil doesn't need to be all that thick for an oil pump to be in pressure relief at cold idle. On typical engine, the oil pump may be bypassing on cold start with room temperature oil. In any case, I was mostly concerned with colder starts when oil pressure buildup is more critical, at temperatures where any oil pump will be bypassing.
I would say it's not "typical" for an oil pump to hit pressure relief on a cold start-up with "room temperature" oil, unless you're really revving up the engine. Room temperature implies 68-70F.
I don't think oil pressure will take much if any longer to build on a very cold start-up unless the wrong oil "W" rating is used, and the pump actually has problems with the pumpability of the oil. The oiling system should remain full of oil unless the filter's ADBV is not working correctly, so as soon as the pump is turning, it's moving oil and sending oil to the oiling system.