I think if the FB page is merely a vehicle for updates regarding this site and encouraging new BYTers to check us out, I would have no problem with it. However, there is no way of knowing that this would be the case. This site works so well because people are interested in asking questions and sharing knowledge. Selfishly, I want that info to be in one, easy to find place - here. The risk of an active FB page, as I see it, is that this site is diminished. Many people are so used to FB that it perhaps becomes the go-to place - either because people feel more comfortable posting there, or just don't want to join another forum. As I say, if it encourages others to seek this site out, I'm all for it. I just don't know whether that's all it will do, nor how anything more could be prevented. I'm concerned there's a chance of being spread too thinly.
That's the difference between a Facebook PAGE and a Facebook GROUP. Groups are for discussions (which suck on Facebook). Pages are just for the owner of the page to post things (like 99% of the other facebook pages out there) but aren't for active discussions.
Sure, users can post on a facebook page but it doesn't show up on the front page and rarely gets much conversation going so it wouldn't affect these forums at all.