In otherwords can I build up the thinset that much in the old wallpaper areas where I flat trowel it on? What you can do is first remove any wallpaper. If you don't, you'll see your tile come back down, most likely before you're even done grouting. Secondly, use a long trowel-- 13 or 14", and you can first trowel on the old thinset areas to flatten them out, and then use the long rowel to feather thinset from those areas down to nothing above them. Then nobody don see NODDING!! :-) Any problem with the thinset going over the torn wallboard areas? The only torn wallboard areas I saw were only down to the brown paper underneath. If that's the worst of it, or maybe a few small areas down to the gypsum, that would be fine to go over. If you have any areas much bigger than a quarter down to the gypsum, though, you might want to patch the wallboard where needed.

It's a heck of a lot easier to remove it all in one piece than it is to try to laboriously patch all the holes that removing it piecemeal would entail. (It also lets you more easily run the wires to your new undercabinet lights.) You can just replace it with a large single patch of either drywall or cement board, prime it, and be done and ready for the new backsplash on top of it.

Have you considered wallpaper? You can bring in color, as well as a design, if that's your 'schtick'. Just throwing another consideration in the mix. I personally *hate* a backsplast covered in tile or granite from countertop to bottom of cabinets, or even further up. I've gone *about* 3/4 up the wall, with the remained just the neutral color thruout the rest of my home, but only on the interior cabs, so above the stove and sink areas. On the perimeter bank of cabinets, it's just a painted wall, where I had planned to use wallpaper, but haven't done so yet. I also picked up at an auction a painted canvass, which is long and narrow, and thought of using it here. It's a vintage French scene of a girl feeding chickens in a barn, done in dark colors, which is my preference. I just don't want to leave it should I sell. ;)

Did they mount upper cabinets on top of the tile? If not, whoever laid these is an ARTIST because those cutouts are pristine. If the cabinets are on top of tile then it all just got a lot harder. At the risk of inducing scope creep, if you do this work to the backsplash then you might want to check on the cost of refreshing the laminate counters while everything is torn apart. For the answer to the original question I would ask a plasterer, honestly.