A leaking tank was an exercise presented to me once in RAF days and the procedure there was indeed exactly that - 'use it before you lose it'. There was no 'drill', just human logic.
That, (as a 737 pilot) is where I see the great divide. I have recently heard from an ex AB pilot (so this is very much 3rd-hand) of an AB 'event' where up popped the ECAM saying (in blue) 'Shut down engine using xxx button' (I'm not familiar with a/c!). The crew did just that. I am told the message actually meant 'when/if you shut down the engine, use the xx button' as apparently that would be the only way. The Boeing philosophy is to rely, as JD says, on 'knowledge'.
I'm sure somewhere I have seen a statement that a 737 will be controllable with one wing-tank full and one empty. I assume a low-speed handling check would be prudent in arriving at a Vref! C of G wise, as barit says, you are eventually going the right way on lateral balance, and I doubt you could get to a serious longitudinal C of G problem. My personal inclination would be to feed both off one tank if I was fuel critical - ie tight ETOPS, at least to use as much leaking fuel as possible (down to a prudent amount) and if possible it would be worth stopping every now and then to see if the fuel level has dropped below the 'hole'.
JD's scenario is one where there is no manufacturer's 'drill'. The only one is 'Engine fuel leak'. That will get you home UNLESS you do not have enough and there is nowhere else to land. There have to be some situations in flying where you make up your own solution.
