Reverend, no they do not but they do use references from the show. The Crossover comic that was written by Ian Boothby relied heavily on stuff from the show as its setup to get both the Simpsons and Futurama universes together.
Patric Verrone has done one issue of the comics (11) and from what I have heard it was an unused idea from the show. He is scheduled to be the writer for issue 14 coming out later this month (or perhpas early next) and I would bet it is another unused idea from the show. He is also scheduled to appear as part of the Bongo Comics panel in SD so my guess is that he will become a regular contributor to the series so we can expect to see more show ideas and development of characters from show themes. It is an exciting time to be on board with Futurama Comics!!