Does pilot-controlled lighting work if you are interrupted by another voice transmission?
From a technical standpoint, it's extremely difficult to tell two different signals on the same frequency apart. So, if someone steps on you while you're trying to turn the lights on, then the ground equipment can't tell the difference between their radio and yours. So, unless the other radio is far enough away that it doesn't register on the PCL receiver at all*, it won't activate. You'll just have to try again when the other pilot's done talking.

In general, it's usually nothing to worry about, because the other pilot(s) nearby will hear you clicking, and know to avoid using their radio until you're done.

* Many airports turn the sensitivity on their PCL down so that distant planes on the same frequency won't interfere with a local pilot trying to land.