No, it's highly unlikely, at least not in the same manner, because they're for-profit companies. Steemit, at least in it's current iteration, doesn't really have a profit model built in. The "profit" comes from the ownership of STEEM and the continued speculative value of the market demand.
Facebook could do something similar to that and hold a portion of the assets. However, this would likely come at the cost of their current revenue model.
I just simply do not see this happening. There are really way too many factors.
I agree with much of what you said. I'm not contesting the economics of steemit or how profit is made. If I were to play devils advocate I'd argue that facebook, if they choose to adopt a similar reward system - introduce a fb share backed currency or tokens etc.. they could severely diminish the appeal of steemit to main street.
Why would millions flock to steemit when they could remain in fb or other social networks with their friends/followers they've built up over many years? For example, as much as I love Steemit (the short time I've been on it) if facebook suddenly implemented doller rewards for popular posts or curating, steemit couldn't compete!
Personally I think they'll have no choice but to monetize facebook for their users or will go the way of myspace and bebo. For me the question is when that time comes, how big will steemit be.