where is it leaking from?
Does it leak all the time or just when you flush it?
If it leaks all the time check the angle stop, supply line, and the tank to bowl bolts
If it leaks when you flush it check the tank to bowl gasket, wax ring
If the water closet was removed to tile the floor and none of these identify the problem it is possible the toilet is cracked
Once you have corrected the leak, and if the grout is not cracked, you should be ok but the moisture may change the colour of the grout after it is dried. Grout is a cosmetic product..not a structural one.