Yeah, that shouldn’t be too hard to accomplish by using the Facebook and Discourse APIs. It could easily be made to work the other way around as well, with Discourse posts being automagically posted to Facebook, if you’d rather use Discourse as your primary content outlet.
Two-way sync is incredibly difficult to do right. I’ve seen serious attempts at it before, e.g. Social for WordPress, and it just doesn’t pan out well. It’s always prone to data loss/duplication and immensely difficult to maintain.
There’s also nothing inherently wrong about having conversations happening in a few different places as long as there are enough participants to sustain the exchange in each “club house”. Every social network or forum comes with its own norms of participation, so you might as well treat them as different schools of thought that you are eliciting feedback from.