I doubt it will cause any problems. The tile is only 1/8" thick, right?
It should have no effect whether if the toilet was removed or not. As
long as its caulked right. Does not have to be pretty, just waterproof.
The only problem I could see in the future is if one day you replace
the toilet, and the new one has a smaller base the the original, it
will show where the cuts were.