Thanks everyone. I got tied up yesterday and almost forgot about this thread. I'll see if I can get pictures and post them this evening. This is a kitchen backsplash.
When I posted, I hadn't removed the old tile yet. Now I have and the damage isn't as bad as I feared, but there is definitely some. There is a small place where I got too aggressive with my bar and put a hole in it, but otherwise the damage isn't too bad. However, there are places where the paper is torn, other places with residual mastick and the old tile goes over a horizontal seam in the drywall and there are places where the old mud tore out. So, its all pretty rough.
The other issue is the area behind the stove, where a previous owner had glued laminate to the drywall. Removing that completely, tore off the outer paper layer of the drywall. Also, the old counter top is a standard premade laminate with the built in 4-5 inch backsplash, and that was glued to the wall as well, so removing it removed the paper as well.
I like the idea of the hardi board. If I smooth the existing wall as much as possible and then put up 1/4 inch hardi board would that solve my problems?