No, I don't think the frame pictured would need to be modified. I have a QR seatpost binder on my junky commuter bike that is just the through-bolt, nut, and the QR lever...kind of like what you have pictured above but without the collar around the seat tube. It just clamps against the binder brazons instead of having a traditional binder nut/bolt in there.

I would caution however...frequently, when I'm riding that bike and wearing baggy shorts, the shorts leg will catch/snag on the QR handle. It has to be kept tight enough so that you don't accidently open the QR and experience a rapid descent in seat height (resulting in possible crash). Or, if it's tight enough to prevent that, depending on how hard you're peddling, then you run the risk of tearing your shorts.

Dan