I think they could. The facebook model rules out certain kinds of very common social interaction. There are certain things you only say or share when you're pretty sure of some privacy (or otherwise drunk). I would argue that there's definitely a need for a network that enables those kinds of interactions even if the demand isn't obvious yet.
That being said, I'm not sure "Christian Facebook" encourages or supports those use cases. I'd like to see more discretion-oriented (end-to-end encryption, read-receipts, retracting sent messages, etc.) features on a service that aims to serve Christian use cases.
I think there is a lot of potential for creativity to be expressed, to come up with new ways to communicate.
The surrealists did automatic drawing with one another, and some folks at Google combined vast quantities of depersonalized data and individuated constructions of layered learning, to create surrealistic like images.
But if you want to reconnect with old friends or announce that you just got a book published or something, you'll still probably post to Facebook.
Then again, I could see facebook being disrupted by a family of special-purpose tools and sites the meet all the same needs. It happened to newspapers when classifieds, opinion pieces, sports news, and various other use cases each went to different internet sites.