It sure looks like your C came from the factory the same as my B. Not surprising during the war years. Most likely it came from the factory with a blanked starter hole. The long toolbox would be the deciding feature for me...must have been a crank-start from the factory and electric was added later. Kinda odd though that whoever did the add-on that they did not also add the generator at the same time. You will need to get two brackets to mount the generator since you probably don't already have them. Plus you may or may not have the proper wiring harness and correct switchbox (with ammeter and special light switch) mounted on the steering column support.
That's an interesting bit of trivia about the taller air intake. I always wondered why mine seemed quite a bit taller than others I have seen. I would be interested in the actual reason why also...I cannot make the connection with steel wheels. You must also have the extended fenders like my B. See picture at link. It is my understanding that this type of fender was unique to the steel-wheel models, common during the war years.