Okay so I had to look them up on Wikipedia...I see them all the time (I live in Texas) but must admit I knew nothing about them. They're insectivores, and mostly eat termites, ants, grubs, and other bugs, but will also eat amphibians, small reptiles, fungi, tubers, and carrion.
They were also hunted during the Great Depression, and in east Texas were commonly called "Hoover Hogs".
I don't see why the occasional armadillo would be bad. They might need to be skinned first, though, or...de-shelled? Not sure a dog could eat their armor.