I've got only one thin barreled rifle that doesn't have a floated barrel, and it didn't seem to like being floated (in an spare short action stock I have), so I put it back in the original stock and it shoots great. Could be that the spare stock was the real problem, but I've just decided to leave well enough alone.
As for the Savage, I'm with the rest. Just shoot the darn thing and see what happens. I would, however, be inclined to ask Savage if the stock is supposed to be touching the barrel. If not, then the action required is obvious.