As Spike12 said above, you should be fine, but I would not expect the same sort of accuracy out of milspec ammo as you would out of commercial .308. One nice thing about the .308/7.62 NATO vs. the .223/5.56 NATO, and that is a commercial chambered .308 has no real issues with the NATO counterpart, but not so with the .223 and it's NATO cousin.I can't see any reason why it shouldn't. There's nothing special about that configuration. It's pretty close to the older NATO standard which should encourage you if anything. Besides, it's impossible to more specific since you haven't stated any type of muzzle velocity or the range you're working with. But if you're talking about an off the shelf commercial load, you should be just fine.
Keep in mind that every rifle made is slightly different. Through experimentation you can find a particular load or ammo that YOUR rifle will do better with than others. Another rifle of the same configuration may or may not do as well with the same stuff.
Military rifles are designed to work best with a specific ammo that is identified in their spec.
Commercial rifles are designed to work with a wide range of ammo. The Ruger American is no different.