The original tiles, unfortunately, are finished (due to a wetting of some parts of the floor because the sump pump failed), the insurance is going to take care of the whole job and if I go with no sub-floor, they will lift off the remaining tiles, clean the floor, apply some kind of sealer, and then install the under pad and carpet. So is this a good alternative to just putting tiles down?
Answer:
I'd rather see you with the peel & stick tiles and a carpet (no under pad in spite of foregoing the warranty because you don't put it in) that is fitted to aesthetically compliment the room than to have all the other stuff around. A carpet with a 12 to 24" boarder of tiles can look nice if chosen with care. The floor will be no warmer with a sub-floor than with a carpet right on the concrete.