First, Join the NMLRA< and a get a copy of their rule book. It will tell you what is acceptable in Smoothbore events. I don't recall there being a restriction against Percussion guns, although at some matches, they may shoot in their own category. The other restrictions will often restrict or prohibit the use of plastic wads to hold the shot, to regulate the size of shot used on a given match course, and sometimes, now, I see restrictions on even using synthetic wads for overpowder or cushion wads. Some clubs don't like the clean up required by using something that is not biodegrable, since they function with volunteer labor just to keep their doors open.
Most Fowlers are going to be flintlocks, just because that is the period of time when they were in the hay-day of popularity on the frontier along the Eastern Coast. Single Percussion shotguns came into being in the 1830 and 40s, as they could be assembled fairly cheaply, compared to double barrel guns, and could be used for hunting and self defense. Because the bores were large, the round ball they shot was heavy and could give good performance against man or beast at 75 yds and under. They were good working guns, usually without the frills and carvings found on more expensive shotguns.