Apps like UC Browser and Opera Mini have been doing it even before we had smartphones. I still use UC Browser here as 2G is really slow. So the bandwidth used will be miniscule.
It's definitely possible for Facebook. In fact they've almost done it. The fact that they won't go the extra step and still insist on calling it "Internet.org" makes me suspicious of their intentions.
Let them go ahead. Call it Facebook.org and cut out the sanctimonious tone of pretending that it's charity.