The computer won't care if the USB is drawing power over the 5V line. There's no data on that wire.
It definitely will care if GND isn't connected. There may be another ground elsewhere but it's vital for signal grounds to follow the signal wires with the USB data.
What happened when you tried it?
I think the Leonardo is the same size and shape as an UNO but it uses the micro USB connector. You could probably find an off-brand UNO which does, since those full-size USB-B cables were obsolete a long time ago.