Except your overflow box isn't necessarily level with (or higher than) the rim of the tank. On my tank, for example, my overflow box sits below the rim of the tank. If I shut off the drain (and plug the emergency drain), water will get pumped into the DT, flow out to the overflow box and then pour over the side of it. Don't get me wrong, I still have a little bit of time and it'll still hold some of the extra water but the extra capacity that my DT can hold is the difference between the (current) water level and the top of the overflow box, not the top of the tank.
It should be noted, however, that I have a rimmed (and drilled) tank so my overflow box can't make it all the way to the top. If you have a rimless tank, YMMV and I haven't given any thought to what happens when you have an over the top/siphon type overflow box.
Something that would be interesting, but no doubt come with it's own set of problems would be a bulkhead (or over the top siphon) with a valve in it that would shut off flow to the overflow box when it notices the water stopped draining. That would allow the tank to fill all the way up to the rim and buy you the extra volume.