I suggested a rail as that would use less material, especially if already have the back cut. But extending the back down works too. If you want it to look more open you could add a curve or two angled cuts on the bottom.
What you're trying to prevent here is sideways swaying (racking) or the connection of the sides to the desk top failing if the piece is dragged sideways on the floor. It's kind of a personal decision of how solid do you want the thing to feel and also how much do you trust the quality of the plywood.
I think i'll go ahead and extend it further, i can always use the extra material from the new sheet for something else. Not sure how much more to extend it though. I'd rather not have it go all the way to the floor. The current panel is 6in wide.
Coop and others probably have much more insight into this stuff, but if you were to add a back panel to the bottom cabinet I think the rigidity would increase tremendously and your pocket hole count would be fine. However if the design and aesthetics are locked in then like the others said definitely get some sort apron(s) pretty close to the bottom to help keep it together.
Pocket holes have worked great for the projects I've used them. Especially paired with good ole Titebond II.