I am sure you'll get better advice from people with more experience but my feeling is that once you remove all the pink tile you will find a wall that is not straight and clean because of the dried adhesive still stuck on the walls. Maybe if you can then scrape that all off you could do it but I know the tile will nee a clean, flat surface otherwise it will not all sit flat and I think the new thinset will not stick as well to old thinset (again others have more experience).

Hi folkman - thanks - when I peeled off one of the tiles, to experiment, the adhesive stuck to the tile and I was left with a dry wall that looked like a brown paper bag. So it was flat and smooth but it really is damaged drywall. I have a feeling the "others with more experience" are going to tell me "NO! can't be done," but we'll see.
Thanks,
Citypigeon

I don't know that I'd say it can't be done, but it wouldn't be adviseable.