I agree that a lot of it comes down to the cleanliness maintained, the lapped condition of the bore, and the stress remaining in the barrel. But these are qualifiers that can't be overlooked, or assumed away with factory barrels and common cleaning.
I have 3 guns so far that will put a cold clean bore shot within 1/2moa accurate.
But all 3 will do better cold -while fouled.
All 3 will GROUP better fouled and brought up to stable temps(better than cold grouping).
And forget cold -clean- grouping. That would suck.
I've had other guns in the past that walk as they heat up & that throw fliers until fouled. Some of my barrels would copper foul out.
But I've managed to take all but one of them to better 'cold pre-fouled' accuracy. The one offender, hot grouped excellent, but walked shots from cold(a T2K, tube
I agree also that carbon must be rigorously managed.
I clean to white metal after every use, no matter how many shots fired. Then I dry pre-foul bores with tungsten disulphide(WS2)(my bullets are coated also).
With this, I can count on my first cold pre-fouled shot being with any to follow.
I do not agree with the assertion that copper should be left in a bore. I don't, I rarely get any copper in my bores anymore, and I just prefer it stay that way.
Other than taking a bore to a pre-fouled state, I think you would just have to try it & see.