Never assume predators aren't prowling around during the day. They might not be as active, but they're definitely there. The last thing I chased off was a young coyote in the afternoon, eyeing the chickens.
Fully covering the run would be the safest option. Electric is also an option. Or you just take your chances, and the chickens will be safe until they're not.
The other question, is will the chickens stay in the run? You might have to trim their wing feathers to keep them in. A net over the top of the run might help with that, and with any hawks you might have.