So you want to break into the video game industry (you want a game biz job). First, you have to know which type of job you want -- if you don't know which you want, you need to read about the game industry and the types of jobs in it. Then you might need to make a decision. Third, you need to be qualified for the job. Fourth, you need to know how to find information and how to ask good questions (you need to not ask bad questions). Finally, we have tips for getting the job.
Would this be a bad idea? I have a project that has some pretty polished gameplay, but I haven't completed it's content yet. I want to apply for a game programming job and I've finished one other game project, and this one's about half way finished. I don't think one game would be enough but this one is half done. I'm probably going to have some other stuff one my demo reel as well (small demo projects like graphics demos, physics, etc).
As long as it's yours, you're free to show it in your portfolio.
In general, it's not good to include stuff you have to apologize for or "explain," but if that's all you've got, go for it. Also you can put a link in your cover email and say "here's what I'm working on currently." No apologies necessary.
-- Tom Sloper Sloperama Productions Making games fun and getting them done. www.sloperama.com
Please do not PM me. My email address is easy to find, but note that I do not give private advice.
In my opinion, it depends on what your part is. For example, if the game's halfway there but you have a song or a character model or game engine to go with the game, those pieces would still be good to include. Nothing you should have to explain or rationalize unless there's a good reason for it.