Yes they are accurate. No, you cannot take a lot of shots in a row with any rifle.
Every rifle barrel heats up, and will start to print all over the target as things get warm. Most of mine shoot best with 3 shots, 5 is starting to push it. Besides, most matches allow a time limit to make your shots. Spread your shots out to allow it to cool. But if your serious about target matches, a Mossberg ATR is not going to be the rifle for you anyways. They aren't made for that. They are a good entry level hunting rifle. Not a bench rifle. Save your pennies and buy a dedicated competition rifle, and don't abuse it. Cool your barrel and your scores will improve.