You can install the self adhesive tile around the edge of the toilet without removing it, but you will be able to see the gap, the toilet may not sit level if you tear up the floor below and not remove the toilet and cutting out the profile may be harder than just removing the stool.
You can calck around the edges with a white silicone calck to cover some of these problems.
The professional way would include removing the toilet first, it all depends on how you want it to look.