Since mine puts every shot in a small ragged hole from a bench rest; I'm not sure that it would make much difference. Fre-floating the barrel would do more, and the foam may stiffen the fore-end.
Likewise, trigger setup is more important as well. You may have to enlarge the opening in the trigger-guard sub-plate to allow the trigger to travel fully forward so you can adjust the trigger set screw. On two of three rifles I had, I would not set up the triggers as this plate was depressing the trigger past the sear release point when I tried to adjust the slack and creep out of it. I enlarged these forward with a file, and was then able to adjust. Once adjusted, make sure the rifle is unloaded, and bang the butt on the floor, if it releases, the trigger is too light. Once adjusted, put locktite on the trigger adjust screw.