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 saw a TV show where a guillotine was built with a blade that swung in an arc so that multiple people could be executed at once. As an added bonus there were nice ratcheting noises as the blade was cranked into position.