I doubt a standard M1A would be accurate enough, even if fit with the best barrel available. Accuracy varies across them and will typically be about 1 inch at 100 yards, 10 to 15 inches at 600. To say nothing of the standard 5-pound trigger; it's a long ways from being able to shoot well with. And the standard rear sight on them has 1/2 MOA or more of windage and elevation slop; add that to the rifle's inheirant accuracy and things get even worse.
A completely reworked M1A with good handloads using new cases (never reload fired cases from a service rifle; they will not be as accurate as new ones) will be much more accurate. The best of them will shoot under 5 inches at 600 yards with proper handloads. But for the same cost, one could get a bolt action rifle that shot more accurate and be able to shoot the same cases over and over. And you wouldn't have to find magazines that produced best accuracy.
The commercial M1A rifle from Springfield Armory was never the "National Match" version of the military M14 rifle. Thompson-Ramo-Woolridge made the M14 National Match version (stamped on the hump, "M14NM") for the US armed forces and was a semiauto only version that could not accept the full auto kit. The M1A is a commercial version of this rifle, but not normally made to the same specifications.