Please don't shoot me for wanting to thwart a rose bush.

My neighbor has a very aggressive type of rose bush that keeps suckering under the fence line. The deer are eating it on her side, so it really WANTS to live on my side. And boy, does it keep trying. I'm allergic to the scratches and want non-thorny perennials where it keeps trying to take over the world.

If I sink tiles into the ground by this bush, will it stop the suckers from coming into my garden?