Using empty peat moss roller to push seed down after overseeding. CT.

I don’t want to buy a $200 roller drum to push seeds down after overseeding. I do have a wire mesh peat moss spreader. I can roll that empty to try to push some down or loosen the seeds down? Is that good enough? Has anyone tried? Does it matter? I have 1/2 acre and want to make this easier for my back.