I recommend removing the toilet; it is not that hard. Shut off the water supply, remove the top section by unscrewing the connecting bolts and use a turkey baster to suction as much of the water from the bowel as possible. Then unscrew the bowel from the flange and pour as much of the left over water as you can into a bowel. It is likely that the level of your new tile will be above the top of the flange. If that is the case, I recommend having a plumber remove the flange so that you can tile right up to the opening in the floor. Then, a new flange slides into the pipe and rests onto the new tile. Drill or chip out small holes under the screw holes in the flange and screw the flange through the holes in the new tile and into your subflooring. You may have to use 2 or 3 inch screws. This way the toilet will be secured to the flange which will, in turn, be secured to the floor. That will prevent the toilet from rocking and breaking the wax seal. I have kids and am glad that I went to this trouble, as I know that the toilet will never loosen from its base.