I think you’re correct… it’s impossible using conventional/linear electrical measurements.
Interesting, but I’m not even sure this would work. There might be a small discontinuity in the delta measurement when the first winding opens. But of course, even if it did work, it’s assumed any technique must be nondestructive. 
Using the saturation of the cores will work. That won’t involve killing the motor. More when I get home 
OK, I’m pretty sure this will work.
Across two terminals measure the DC resistance.
Now you need a setup that allows you to push a hefty DC current through the motor with a variable voltage, and to superimpose an AC voltage on that. Connect it up and use it to measure the complex impedance across the two terminals.
Now ramp up the DC component of the drive. You should see no change to the impedance until the core of some of the coil saturate.
If the motor is wired as a Y the two coils in series will have saturated, and you will see a residual complex impedance made up of the coil as if it had an air core along with its DC resistance. Which will be the DC resistance initially measured.
If the motor is wired as a delta only one of the three coils will have saturated, as it will have been taking 2/3rds of the current. So the new impedance will be made up of 1.5 times the DC resistance initially measured in parallel with twice the initially found inductance in series with 3 times initial DC resistance.
If you continue to ramp up the DC current, the Y connection will remain with the same impedance. The delta connection will eventually undergo a second collapse in impedance when the current is tripled, and the second leg saturates. This may provide a confirmation of the Y versus delta, but may need more current than is sane, sensible or safe.
Wow, thank FV. May just work. 
Am going to run this by some folks at work to get their opinion.