The roots are dense and deep. I don't think you'd kill the grass, it could come back, and you might accidentally start a grass fire. You'd be held responsible for that if it got off of your property, so I'd recommend you take the conservative route and dig it out.
Hello Neighbor in Ft Worth -
I am not worried about the fire. I will make sure either to carry water and burlap or to wait till it rains. I just want to know if it will work. Digging it out will have me outside till next year. Seriously. I have done a little of that. In some places it is just about solid.