Why wouldn't it work? A double agent, or whatever you might call it, could be always worked into the overall game plot.
Now that you mention fight, I have realized that Jazz didn't get into any 'real' fights as well. I don't think he has used his cannons for anything but the zombies, as far as I can remember.
If nothing can be worked out we could create a duelling club, so that all characters that need to get off some steam can go at each other. Could be quite liberating for them.