I'm no expert, but since nobody else has yet replied...
I'd imagine that if you cut both vcc and gnd on the USB cable, your data pins wouldn't work as they'd have no reference to ground on your Nano. Cutting just VCC on the USB supply should work.
I've never ran vin and USB myself, but as a complete noob's guess, I'd imagine the two switch mode supplies would inevitably be out of phase and cause all sort of AC noise on vin. Apart from that I don't think it would be a problem, BUT, that's only my semi-educated guess and it's not worth risking your PC's motherboard on. 