Now, you wouldn’t want to leave this on the grass in any depth, as it would smother the undergrowth. Also, decomposition requires nitrogen, which is exactly the nutrient needed most by leafy greens like grass.
That being said, the tiniest pieces have all winter to break down. Raking up the larger morsels and popping them on your garden is a way to get the best of both worlds.
On the way back home from the dog park, we met the guy on the rider mower doing the same thing at the public school across the way. It’s usually left for the sweeper to pick up for the city compost heap. Before it disappears, we’re going to get us some o’ that.