I can think of two ways, although i've only tried one;
the way i've done it in the past is just to set up a parallel bus for the vocals with distortion on an blend it back in with the dry one.
However, and this is just guess work/logical thinking, you could do the same thing but put a noise gate before the distortion plugin on the parallel bus so that the distortion only kicks in when the vocal crosses the threshold
just a thought
In the world of music there's no right or wrong, however there is "tried and tested" and "experimental"