Perhaps not with that kind of packed ground. We have sand ground cover in the coop and run with hard, packed earth under. This hasn't been a problem with predators, but with the chickens lol. Ours hate being cooped up and have started trying to dig a tunnel under the run.
I would definitely consider covering your entire run in 1/2 inch hardware cloth tied together really securely with either wire or zip ties. It's pretty expensive (if I'm remembering correctly, it cost $500 to do our coop and run), but will save you from heartache. Predators (we have stray...