I don't see why not, they pick up leaves

I'd be concerned that wet grass could clog up the machine. When leaves a vacuumed up they are much drier. Another consideration is the weight... a leaf vacuum bag full of leaves is pretty heavy one of grass clippings would be even heavier. Vacuuming, whether of leaves or grass on a gravel path can result in the gravel being sucked up and cause damage to the machine. We learnt this from experience!