Indeed it does, and by far the best way of doing it. You do not want to have a propeller-synchronization failure with one of those things. It is fascinating how many innovations mentioned here originated, possibly in less practical form, in WW1 or even earlier. Gottlieb Daimler, for example, patented forced induction long before anybody knew if the internal combustion engine was going to catch on, and the French had turbocharged aircraft in WW1.
George Guynemer and René Fonck both flew Spads with a short, low-velocity 37mm. cannon fitted in just the same way as the Airacobra's. I have heard unconfirmed reports that Guynemer originated it, but Fonck is reputed to have shot down a considerable of aircraft with it I believe it was the gun used as an infantry weapon, and sometimes a very effective one, although the mortar was surely better, and especially so in the trenches.
I know the Spad's version was hand-loaded, and it was probably the version which someone must surely have called quarter-automatic, for it automatically ejected the fired case, and was then loaded by hand. It was probably as fast firing as the weight-carrying capacity of a WW1 fighter made advisable anyway, but it would be nice to have nothing else to do at the time. I have a vague memory that I have seen a photo of one in the front gunner's cockpit of a very early pusher biplane, which seems like the most practical way to use the thing, but nobody gets famous in one of those.
The Airacobra's drive shaft is variously reported as running under the floor and between the pilot's legs. I don't know which, but the former, or at most between his feet, sounds the more plausible. The rear-engine MB1 was a light civilian aircraft, in which the shaft ran quite high up, between the side-by-side pilot and passenger. Even lightplanes crash sometimes, and two's company in that situation.