If I feed an LM324 with V+ but no ground, what value will I see on the GND pin?
Using a 10M input resistance multimeter, and referring to the datasheet, the schematic:- 



Looks like there's maybe a couple junctions with some resistive stuff between Vcc and GND. 

So if none of the other pins are connected to anything, the GND voltage would probably read around 4.5VDC. If there were low (in relation to 10M) resistance paths to ground from any of the other pins, then I would expect a voltage of about 0.7V (because of the isolation junctions to the grounded substrate). It will be somewhere in that (approximate) range, for sure, assuming nothing else is powered. 

A more precise answer might be the approximate range of +4.5 to Vx+0.7, where Vx is the lowest voltage that appears on any other pin. It could be higher than 4.5 if the DMM was very high input resistance.