Well, chickens do, I can vouch for that personally. Geese probably will, at least when the shoots are young and tender in the spring. Whether or not they'll damage it too much I can't say. I have variegated ribbon grass (Phalaris), 'Heavy Metal' Panic Grass, and a couple of kinds of Miscanthus outside of my chicken run, and they clean up everything within reach, which isn't much since they can't get far through the chicken wire skirting between the boards. A couple of times they managed to rip a hole big enough to get a head through, and enjoyed the ribbon grass, but that species grows back so quickly its hard to even notice.
I am sure it would work out fine. Worst case scenario, you could always make a hardware cloth "shield" to protect the grass from the soil line to above the reach of the geese.