I looked at the LM393 datasheet again. Max output leakage is 1uA with 30V on the output, from 0C to 70C ambient, with Vin- = 0V, Vin+ >= 1V.
I would guess that the same figure holds when VCC = 0V, since there is no voltage to turn on the base of the output transistor. You may even see lower leakage than the spec. The Vin- = 0V, Vin+ >= 1V in the leakage spec is probably there to put Q15 (in Figure 1 in LM393 datasheet) into saturation, in which case the output transistor base voltage is still higher than 0V.
The only way to know for sure is to try it, probably at a higher temperature.