It's a neat idea! My experience with writing Facebook application is pretty limited so I'm not sure how much power you have over posting updates into groups on behalf of all users of the group, but in general they have pretty robust capabilities for applications so I could imagine it working. Some of the problems you'll run into:

1) Obvious one: we don't currently support adding new messages through the API, as you noted. It's on our roadmap (ie, the real group roadmap, not my "if I have spare time" roadmap), so it's likely to happen before the Football season rolls through, but I don't think I'd be able to guarantee anything. Without that, you can still pull the messaging and transactions into Facebook (since we have GET APIs), but it wouldn't feel as coherent if you couldn't use the same interface to push messages back. If you pushed Facebook comments into the Yahoo! message board, though, you'd also have to worry about not duplicating the messages back into Facebook again once they're on our site. Not impossible to solve by any means, but probably a bit annoying. Maybe you'd blacklist certain message IDs if you know they were posted through Facebook?
2) Correlating Yahoo! users to Facebook users isn't a trivial problem -- we don't currently expose any facility to match those up, so you'd have to manage all of that within your app. It could probably be done as a manual step, but you'd need to do that on your own if you wanted to have the most likely expected behavior of having a user's comments in Yahoo! show up associated with their Facebook profile data in your group (ie, correct name, photo, etc).
3) We don't have a push architecture for our services, so you'd need to be polling and thus would be guaranteed to have latency between when a message is posted and when it shows up within the Facebook context. Probably fine, just worth noting that we can't get you hooked up to anything like a message/transaction stream, really.
4) And again, because you'd be polling a large list instead of having only updates pushed to you, you would need to track the current state of which messages/transactions you've seen so you know which ones are new and need to have an update pushed to Facebook for them. I think that all of our messages and transactions have IDs, so you could either use that, or just keep track of the last timestamp and compare it to the timestamps for each messages/transaction element.

We do have a small bit of Facebook integration for our Football game that will allow you to Like your League and Team to receive certain updates, but they mostly focus on statistical updates instead of social updates, so there's certainly room to try to build something like you're describing. Even if you can't have the application writing back to Yahoo!, simply having notifications within Facebook of interesting activity by other members of your league sounds compelling.