If you can handle shotgun slugs the 308 will not bother you. The 308 has about the same recoil as a 12 ga field load. If the gun fits you recoil shouldn't be an issue. Moreover, the hog hunter actually has iron sights on it. A bolt on muzzle break might block your view with the iron sights.
I like the hog hunter myself. If I was willing to buy 308 ammo I would own one. The hog hunter would be a great truck gun. Maybe someone I know will buy a hog hunter so I can try it out with steel case ammo. If it will shoot steel case ammo I could swing 500 rounds of brown bear.