It's possible. Facebook will have to do a lot of catching up but the opportunity it has is incredible. The potential is there for Facebook to be a dominant player but they have to move beyond the "I am on my couch drinking tomato soup because I have a runny nose!" crap that too many people feel the need to share. From a data collection POV, facebook will know more about their customers than just about anyone on earth. So the potential is there to make boatloads of money by selling highly targeted ads (e.g. how much will Campbells pay to know that Suzie drinks Tomato soup when she has a cold? Answer: a lot). And only Facebook will have this kind of intimate detailed data about you and your friends. It has a lot of potential on its own. But they have to make sure they keep it sticky - I know some people spend a lot of time on Facebook but I bet its less and less than it was, largely because there are only so many inane comments you can possibly read from people you hardly every see in real life.
So Facebbok might be interested in streaming video service but it is probably not at the top of their list of things to do.
But ultimately it doesn't matter. Because with Facebook going public and working on its advertising programs (you will see more and more very targeted ads appear on your wall that only you can see, not your friends, and you will be able to click to learn more) the fight to capture revenues from web use will just get more intense. GOOG will lose ad dollars to Facebook, so they will need to make that revenue up somewhere else. That is how this fight will begin.
You will have GOOG, MSFT, AMZN, AAPL, and a few others absolutely slugging the crap out of each other. AAPL and GOOG are at it on phones, AMZN and AAPL are at it on pads and movies. NFLX will have to offer up a pay as you go plan to stream new films the way AAPL does if they wish to remain competitive. That will also make them more profitable AND more attractive to a buyer.
YHOO is a marginal player relative to those 4. A YHOO buyout of NFLX is a survival move for YHOO, but in the end it just make YHOO a more attractive buyout from MSFT (or maybe Facebook) and so on. At some point these second tier companies - and yes, NFLX is a second tier company relative to AAPL/AMZN/GOOG/Facebook - will consolidate and/or merge in order to get bought out.