It is possible although I do not think it will totally take off, so to speak. Some is being done because we have a nasty habit of building houses on farmland. There is little enough as there is. We can eat our houses when the crunch comes. But there is also a looming water shortage. I do not know where hydroponics is going to fit in, but it may well be a squeeze.
I used to work at a Meijers store in Ohio; we used to get hydroponically grown tomatoes. They were every bit as good as what came fresh out of a garden and they were available through the winter.
This is trying to cash in on the best of both worlds: growing fish in the water and plants on the water.
Someone here mentioned that this guy has a sump and grows some edible greenie on it. This concept is a little different as the 'sump' is on top rather than on the bottom. It has the advantage that, in case of a power outage, there would be less of a flood as there is less water in the top veggie section.
If I were younger, more ambitious, I'd probably attempt it, most likely with trout.