Just as important as in any other .223!
importance of twist rate does NOT change when you use a different action type. so it's just as important if you're shooting a bolt action prairie dog gun as it is when your shooting an AR-15.
if your bullet weights are 55gr or less, just about any current production factory gun will have a sufficient twist (don't know of anyone even MAKING a 1 in 14 any more) since as long as it's 1 in 12 or tighter it should do all right, for anything up to 65gr get a 1 in 9 or 1 in 8, if you go with the real heavyweights get a 1 in 7.
anyway, twist rate is twist rate, bolt gun, Semi-auto, pump, break open single shot, don't matter. once the bullet is headed down the bore, it doesnt matter one whit how you got the round into the chamber.