I have a covered chicken run that's got a floor of woodchips over dirt.  Now that it's spring  

 we just mowed our front lawn.  The girls don't have access to grass in our suburban backyard they free-range in.  I was going to put a bucket of grass clippings in their run for them to scratch around and eat or whatever they want!  But I'm reading posts and getting mixed messages about if it's a Do or Don't.  The grass clippings seem to all be under 2".  See pic.
And if it is acceptable, should I just dump all the grass clippings in there or limit how much I put in there?  Wondering if it's a good ground layer for the run itself?