Shivan,
Two MOA with an issue M1 is possible, but don't count on it.
USGI Armory spec for the M1 rifle WHEN THEY WERE NEW was that it had to be capable of shooting 8 rounds of M2 ball ammo into 4 MOA or less at 100 yds. If the rifle could not do this, it was sent back for repair.
With a required spec of 4.0 MOA for 8 rds. @ 100 yds, or better, it is apparent that most M1's will do better than that WHEN NEW. In my experience however, most M1's, even when in "like new" condition will not quite make the 2.0 MOA @ 100 you are asking for. Time has taken it's toll and the wood (a tight fit for which is CRITICAL to M1 accuracy) has compressed and loosened. Maybe 20% will shoot this well, and not all the time and not with all ammo. The vast majority of issue grade M1's (and I'm talking here about barrels that meet Service Grade spec, i.e. new to slightly worn.) will shoot M2 ball into 2 to 3-1/2 inches @ 100 yds.
You can better your odds with better ammo. Many M1's will respond positively to tailored handloads using the SMK 150-168 or 175.
You can also better your odds for accuracy with new tightly fitted wood, or by shimming or bedding the action in the wood it comes with. Note that shimming and bedding are not allowed if you plan to shoot in CMP John C. Garand matches. They are allowed in NRA Service Rifle and in CMP EIC (LEG) Matches.
The ultimate in accuracy is to fully upgrade an M1 to "Match Grade" state with a new commercial barrel (Wilson, Douglas, Criterion, and Kreiger all make good ones) new tight wood, fully glass bedded, unitized front end, trigger job, and NM sight set. I own two such rifles and shoot them in NRA Service Rifle and in CMP Leg matches. Both are well capable of less than 2 MOA (the size of the 10 ring) all the way out to 600 yards. One is quite capable of holding the X ring at 600 (1.0 MOA) if I could ever tighten up that loose nut behind the butt. ha :D
BTW, I own LOTS of M1 rifles. All bought from the CMP. Most of them have been Service Grade and are what I use in formulating the above stated opinion. ;)
Best of luck,
Swampy
garands forever