If you go with the McMillan Edge stock the biggest difference will be weight reduction. Probably about 1/2 lb. With a standard weight McMillan you may end up with a heavier stock or one of equal weight. I wouldn't expect accuracy to change at all. MOST rifles shoot somewhat better floated, but there are exceptions. If your rifle doesn't shoot well floated it is simple enough to add some pressure back to the fore end.
I no longer own one of the MT rifles. Mine was one of the ADL SS versions made in the early 90's with a factory plastic stock. I tried it in one of the Ti stocks for a while. The Ti was floated, the factory stock was not. Accuracy was about the same. I would put the 1st 2 shots from a cold barrel into almost the same hole. #3 would usually open up to around 1". Any more than 3 shots without several minutes to cool down resulted in 2-3" groups, but was not a problem to me.
FWIW, I really like McMillan stocks. Especially the lightweight Edge versions. I have 3 Winchesters in them. Accuracy is no better than before, but I don't spend $500 on a stock unless the rifle 1st proves it is a good shooter so there wasn't much room to improve. They are right at 1/2 lb lighter than before, and much tougher than factory. The quality, fit and balance are worth the cost to me.