I was just listening to one of MB's podcasts and he was talking about the Ruger Rimfire Shooting Competitions and he was saying that there are classes for just about every type of .22 rifle (bolt, lever, pump, semi-auto). If all you have is a bolt gun, I don't see why they would stop you from using it. Doing so would discourage people from participating because they would feel like they would have to spend money just to try it.
Ultimately we want people to come to competitions and shoot, so what if it isn't the latest and greatest firearm. If they have fun and enjoy themselves, they are more likely to continue and will spread the word about it.