I have a 4x7 (footprint) tractor. With just 2 hens in it, they make a noticeable impact on the lawn in just 1 day, really obvious mess in 2-3 days (takes about a month to get back to looking indistinguishable from rest of lawn), and virtually bare dirt in 4-6 days.
This is on a reasonably healthy, reasonably rapidly growing lawn.
I did leave the tractor, with 3 hens in it at the time, in one place for like 3-4 weeks once. OMG, I thought the grass would never come back. But a few months later, the only sign was a slightly brighter-green rectangle of grass.
So unless you want a giant mess, you'll have to move a 6-hen tractor daily. Whether and how well your grass comes back if you let it go to bare earth will depend on what kind of grass you have, some has much less of a sense of humor about that sort of thing. A typical fescue/bluegrass lawn is real hard to kill outright, though it may look awful for some months.
Good luck, have fun,
Pat