Japanning is just an old fashioned semi-high temperature paint. If the japanning is not well bonded to the base metal, electro is going to lift it off, just like it would with any other paint. I don't think we understand exactly how molasses removes rust, but I think it is a good assumption that if there is rust under the japanning, and that is what the japanning is adhering to, molasses will result in a loss of the finish. If the japanning is tightly bonded to the iron, it is reasonable to think that molasses won't damage it . . . much . . . but the standard disclaimers apply. You know, "test this product in an inconspicuous location first."
It seems a bit strange that these pots would be japanned at the factory. Spittoons, waffle iron frames, mail boxes, tobacco cutters, and fruit press frames were japanned, but I am not familiar with pots being japanned. Do you suppose someone might have painted them to pretty them up a bit?