Often times it will. Under optimum conditions, up to 97% of the fading of the tattoo can be accomplished. However, since the doctor cannot know the exact specifics on the ink used, how deep the ink is below the skin, and how much was used; it is impossible to predict the exact degree of removal of any specifc tattoo.
Some ink colors respond better than others. Dark blue/ black inks typically respond and fade very well. Purple and orange inks also fade very well.
Green and yellow inks are the most difficult to remove.