I would say, yes. It serves two different purposes.
Buried wire is to prevent predators from digging under and into the run. It can also be attached to the run wall at the bottom and left on top of the ground, if burying it is a problem. You can stake it down if you need to.
Putting wire with smaller holes around the bottom section of the run, several feet up from the ground, is to keep raccoons from reaching through and dismembering a chicken. Chickens like to rest against the wire or come over because they're curious. It's also to keep curious chickens from sticking their heads out and getting killed by predators. Unfortunately, they just have no idea that they are doing something that will get them killed. This can happen with predators like dogs or foxes, too.