The heart of the question is whether or not it matters that the gunship airplane is travelling in a circular path. No it does not. All that matters is the aircraft's instantaneous linear velocity at the instant the bullet leaves the muzzle of the gun.
Some of the answers addressed the effect of the spinning barrel assembly of a Gatling-gun type weapon. This doesn't really appear to be what the question was about, but the same principal applies: the instantaneous linear velocity of the barrel at the instant the bullet leaves the muzzle will affect the bullet's trajectory. To know what direction the barrel is travelling at the instant the bullet leaves the gun, we have to know how long it takes the bullet or shell to pass through the barrel, and how quickly the barrel assembly is spinning. If rate of spin of the barrel assembly is not constant, the effect of the barrel's motion on the bullet's trajectory will not be constant.
This Wikipedia page mentions a firing rate of 1,800 rounds per minute for one of the Gatling-gun weapons used on the AC-130U. Since there are 5 barrels, the rate of spin of the barrel assembly must one fifth of this figure, or 360 revolutions per minute. Assuming that each barrel assembly rotates around a circular path with a diameter of 8 inches, i.e. a radius of 4 inches (a wild guess), the instantaneous linear speed of each barrel due to this rotation is about 9043 inches per minute or 8.6 mph. This appears to be a rather trivial number compared to the flight speed of the aircraft. (To correct this estimate for a different known radius of spin, divide by 4 and multiply by actual radius of spin in inches.)
If we assume that the bullet is fired at either the top or the bottom of barrel's circular path, and we assume that the barrel only travels a short distance before the bullet exits the barrel, then the barrel would be travelling roughly horizontally when the bullet leaves the barrel. This would mean that the instantaneous linear velocity of the barrel due to rotation of the barrel assembly should be either added to, or subtracted from, the instantaneous linear velocity of the aircraft, depending on whether the bullet is exiting the barrel at the "top" or the "bottom" of the spinning barrel assembly, and which direction the barrel assembly is spinning, and on which side of the aircraft the gun is mounted (the left side in the case of the AC-130U.)