I don't know for sure, but the material difference wouldn't make much difference heat wise.
From my experience, the Issue with stainless is you can only get thinner metals, and most common stainless (304-316) aren't that great for exhausts, they have a hardness that seems to equate to a high resonance (might be how you explain it, idk) so tend to give off more noise with the exhaust, so they can sound a bit cammy or ticky up front, especially when cold. That's why BMW double wall their stainless exhausts in some cases to cut the noise, it's also good for heat -but that's another discussion haha.
The other issue with stainless headers, is the tenancy to crack, but that depends how they are made more than anything, but standard mild steels (ie boiler tube) is more forgiving for such, and quieter noise wise.
A mild steel exhaust is a must for coating, due to the rust factor.
Could get away with it, if you went stainless, but I'd still coat them for the thermal property reductions.