Lots of people do that blondelle. It would be wise to install a vent/fan though

It will be good to have a vent/fan. Otherwise you will have condensation running down the painted wall when someone takes long hot showers. Probably won't do damage to the wall if it is prperly painted with the right kind of paint but it can look pretty bad in the long run. Plus you will have all sorts of mold and mildew constantly showing up in there.

I think it makes sense to tile behind the toilet. The little square of wall right behind the tank seems to get kind of nasty when it's just drywall, and since you will be repainting fairly often you wouldn't have to paint all around the toilet, which requires getting down on the floor, not one of my favorite things to do. The new bathrooms in my houses are getting tile wainscoting.