I think this is a real valid concern, and please post the results as I'm getting ready to put mine in the same stock and start the build up on it soon.
To me the more you can do to "firm up" the bedding, the more repeatable and less problematic in the future. As C Ward pointed out the action isn't overly robust to begin with and I could definitely see how it would loosen up over time in a wood stock. Heck I did some minor stock work on my mom's hunting rifle last week (late 60's Winchester Mod 100) and was shocked at how sloppy the action/stock fit has become over time.