Grass seed is cheap. Try it.

My grey squirrels are good at planting walnut trees and I am good at cutting them down and converting to mulch. I have been using it as a mulch for over 20 years with no noticeable negative consequences. Of course I have never mulched turf grass. Where you are tilling it into your soil, you may want to add a little additional nitrogen to make up for the decomposing wood chips consuming some in the process. Al

Dont use it in your garden. It is toxic to tomatoes.