Hi 1longshot,
A friend of mine has a Winchester 70 Featherweight in .308, it's Oh about 10 years old now, blued and walnut but it shoots very well. If you continue to fire quickly, yes it will move POI some. He does not hunt and only uses it on the range. Thinks nothing of shooting 20 shots one after the other and OK it won't do MOA under these circumstances but it's certainly not inaccurate.
If they have changed the way they make them I cannot comment on, but this Win Featherweigh impressed me, it really did. I have shot it and it's lively from a prone postion using 150 Grn Federal American eagle cartridges.