Sure, but you have to have enough momentum to cut through 15 necks consecutively. Spines do provide a considerable amount of resistance that must be accounted for.
How about a circular design, with a spinniing blade?
If timed correctly, individuals could be removed and replaced within time for the blade to come around again, thus creating a near infinite stream of headless billionaires.
I am assuming the spinning blade would have to be powered by electricity. Makes it unreliable in the inevitable blackouts that helped lead up to the mass revolts. I can't imagine we would execute the billionaires without hitting a breaking point first. I imagine a lack of electricity will hit before mass starvation.
I'm away from my solidworks right now, but I only had the idea because of a TV show I watched a few episodes of where a 5-person guillotine was used. It had a long arm with a blade that would swing in an arc, 90 degrees or so in total. They would set the machine by cranking the arm up into position. It wasn't ever shown if it was weights or springs, but the show was set in a sort of Victorian Era fantasy world. "Carnival Row" I think was the name of the show. There were faries and satyr and some humans that desperately needed to be guillotined in the town square.