CS tiles are better than the storebought's factory ones. I've washed my cube a couple of times in the dishwasher with the original ones, so I think you will have no problems with yours.
Heck, I accidentally left my cube in my pocket and it went through the washing machine, and the textured tiles I had on it made it through OK. It should be fine
i dont think they can "wear off", but i think that in the hot water the tile adhesive can stop sticking the tile to the piece and the tile fall off the piece
p.s. in my dishwasher you put salt or rinse aid or something and the salt will definitely not help the adhesive