I've found that smoking components used in a sauce (like spices, peppers and onions already mentioned above) will give a sauce a more subtle smoky back-flavor than putting a container of sauce in my pit, or adding liquid smoke to an existing sauce.... it seems that the last two options give the entire
sauce a smoky flavor, not a hint of smoky flavor to a sauce that has other flavors in it that I want to taste.
That said, it's possible to attack the solution from another angle. Try adding some liquid smoke to ketchup. Or try putting a pan with ketchup on the pit to soak up smoke. Either way you now have a single component that has a smokey flavor.... the ketchup, and trust me ketchup takes smoke well (both natural and liquid)
Then, when building your sauce, use the smokey ketchup to add a hint of smoke flavor. You will still be able to distinguish onion, garlic or fruity flavors within the sauce, but will get a light smokey back flavor.
Plus the smokey ketchup is great by itself on fries or onion rings.