Perfect, nope...but do it and report back about how we fret over bedding brands shrinkages vs others, etc. If done right and the two actions don't present a binding issue outside of a thou or so in ONLY diameter...it'll shoot just fine. Been there several times. Is it perfect, no, but can you see a difference, also likely NO.
I'm not gonna intentionally bed my comp br rifle to a different action because I have no need to but I think you'll be pleasantly surprised as long as it doesn't bind somewhere. As in, if the 2nd action is smaller everywhere, I'm literally betting I can't shoot the difference. Check it when done with an indicator!!!
Lets not get into tune. It might take a slight retune or might not.
One of the better known rf smiths(for a while) claimed to be able to mill the inlet well enough that his stocks didn't need bedding at all. Well, to a LIMITED point, I agree with him but there are factors that statement on it's own can't and doesn't account for. Which is why I would not ever make that claim. It's like guaranteeing factory ammo to shoot...You're guaranteeing someone else's work and staking your own reputation on that claim. Not for me.