That‘s a bit marginal, but since this is the first jam I’d say go ahead, and just be sure to mention when you started working on it. Personal or third-party frameworks, engines, code snippets etc. are allowed since a number of genres would be almost impossible to build for some of these older platforms in under a month if we all started from scratch.
As for requiring a finished game, this jam will focus more on playable games than polished titles. Anything playable would be great!