Since they can peck greens out of a suet cage Real Well, I cannot imagine they would not be able to peck grass through hardwarecloth. It would have to be pressurewashed daily to wash the poo thru (cuz it isn't going to fall through such small mesh)
And worst of all, to my way of thinking, it would prevent the chickens from scratching around or digging dusting holes. That's what chickens DO, it's what they're made for, it's what they love, I just can't see taking such a basic activity away from them.
Avoid a gigantic patch of mud by ensuring excellent drainage and no water running into the run from elsewhere, and then once it's bare, WHEN THE GROUND IS BONE DRY (not when it's already muddy) put in some sand or gravel, or if you really prefer you can use something organic but you'll have to rake it out and replace it before it starts to decompose into muck. You can still chuck green things in for chickens to eat, such as garden weedings.
JMO,
Pat