I have 8 Kunes, and mine do dig but not deeply, they just roll the turf back and snuffle around underneath. When I move them I'm going to scrape off all the loosened turf and sow beet / turnips / greens / beans there ready for them to return in winter.
They're very friendly and confidant. I don't have an intact male, just gilts and castrates, they all get on very well together and snuggle up into a very small space at night.