Depends on how well it drains. You do not want a run that stays wet for different reasons. The run can get wet even if covered as rain can blow in from the side or rainwater runoff can flow in. That's not a big deal if it dries out in a few days but if it stays wet long enough for anaerobic...
Reminds me of a story. Our dog was laying in the front yard when it was right at freezing. Bright sunshine, very calm (no wind), and frost on the ground. My wife saw her and said, "That dog must be miserable".
The dog was not miserable. She was where she wanted to be. She could have gone...