If you let them rot into the ground, you'll have the best grass ever! A guy I knew ended have a stack of round bales (two high) go bad and never got around to burning/moving them. They rotted into the ground and he said that the grass was incredibly thick and tall in that area.
We did this sort of thing on purpose with our cows with what we call bale grazing. We fed the bales out in the field in a grid, via electric fence. Two years later that area was 4 feet high in grass and alfalfa. The pasture was a 20+ year stand of alfalfa. It works wonders.