I'll delve into this a little further. Specifically Savage actions. One, this is a Savage site and two they're the only action I have a slight knowledge of manufacturing specifics. Notice I said slight

First its my understanding heat treating and quench adds a touch of warp to an action. If thats true its logical to assume the amount of warp would be variable between two different actions.
Then theres the hand polishing station. This area alone would be responsible for the most variables between two seperate actions.

Now you get to the recoil lug. Factory action faces are never perfectly trued which meens the recoil lug will be slightly crooked. Lengths can vary also. So now you have recoil lugs at varying angles and lengths and actions with different contours and warpage.

All that said its probable the bedding job would be better than out of the box factory fit unbedded stock.
I would imagine the action used for bedding would exhibit better accuracy potential. My concern would be using the second action would begin to damage that bedding job and try to form it unto its own dimensions ever so slightly. Bedding is malleable. Some more than others.

Deer rifle accuracy you'd probably never notice. Looking for Benchrest accuracy I'd never swap out an action. JMO