I'm not sure why you'd want to shoot an armadillo, but I don't see why you couldn't. Most of 'em are squished on the side of the road, but I've seen plenty of live ones. Depends on where you are. They're not subtle, so spotting one shouldn't be too tough if there's one around. If you're ever trying to sleep and it sounds like there's a Mack truck rolling through your back yard with the engine off, it's probably an armadillo digging for bugs.
My maternal grandmother had never seen an armadillo, despite having lived in Oklahoma most of her life. She came to stay with us for a while and one wandered up into the yard. I called her out to look at it and she stood outside watching it for 20-30 minutes. Sadly, she's no longer with us (pancreatic cancer about 10 years ago), but she was able to cross "see an armadillo" off her bucket list, at least. They can be entertaining critters, especially when cats and/or dogs are involved (kids with sticks will do). When you poke an armadillo, they tend to jump straight up. They may or may not also whack you with their tail, which stings a bit even through blue jeans, hence the need for a stick.