Nice setup! One thing you may want to seriously consider, though, is putting mesh around and a solid top over your heat pump/AC unit. If you don't, you're gonna have one mell-uv-a-hess with chicken poo and feathers! :D
They aren't likely to get tangled in it unless it's loose, so that's not a major issue. I would be more concerned about them picking at and swallowing any broken strings. Plastic definitely doesn't digest well!
Removing it depends on where it's located. If it's in their enclosed run, I'd pull...