There is a snippet in the article that you linked to which makes a pretty good statement about how effective this is:

“In studies we’ve done, data has shown that both blue and red light have a low efficacy range in acne treatment,” Dr. Alexiades-Armenakas said. “But it took dozens, and I mean dozens — 88 treatments — of the therapy, before we could see any results.”

The referenced study utilized a special set of lights and ointments, and was not simply exposing the skin to blue and red lights.

More importantly, this link claims that the FTC has filed settlements with the manufacturers of these applications, meaning that the apps were making fraudulent claims. http://www.readwriteweb.com/archives/ftc_fines_anti-zit_apps_sold_in_itunes_store.php

In short - no, these apps do not appear to work.