It can help. My ATR in '06 I haven't bedded and it shoots very well. I haven't done much work with it but my reloads usually shoot under 1" at 115 yards. My 4x4 in .338Win didn't shoot as well. Not even close. The way the 4x4 has the magazine holder sandwiched between the action and stock allows it to wiggle when firing. I used JB Weld to bed the magazine holder into the stock and then the action on top of that. It took the groups from 3-5" down to around an inch. Sooo, it may increase the accuracy, but if your ATR already shoots under 1" at 100, you may not gain anything.