FWIW, the jocky-box (or really in this instance it would be a prechiller) would not be my preferred way to go with this, and here's my reasons:
1) You don't really have a way to clean inside the coil after cooling, and because you need to have at least 180F liquid inside the coil for preferrably 2-5min, you could end up with a sticky, gross mess to deal with the next time you brew unless you REALLY clean it out well, which wastes a lot of the water you're trying to save.
2) The inital burst of the hot water will really kill any cold water/ice you'll have in the cooler almost immedately. Running the water from my tap into a catch bucket, the inital temp of the exiting water from my IC is well over 160F, and really takes a fair amount of water to get below 110F (around 2gal or so), where the water starts to cool down. IF you're using the cooler as the cold source, you'll heat up all the ice/water from the inital run before you can get it cold enough to really impact the temp where you need it most (transition from 90F-65F)
3) Break material - I siphon all the wort/break into my fermentors anyway, as I have a ton of space in them and don't care. That said, trying to pass the break material (and hop material if you don't use a hopsack) through a narrow tube to chill it will make for some bottlenecks, possibly clogging it without an easy way to clear it.
Really, if you're looking to save time and not worry about little "helpers" (and I know, I've got two!), no-chill is an AWESOME way to shave time. If anything, with the volumes we're talking about, by the time you get everything cleaned up and put away, you could easily put the 1gal jug into the fridge and come back to it 30min later and pitch.
In short, I think it's a novel idea, but the risk/payout doesn't make it worth pursuing in my opinion.
YMMV, of course.