I doubt you will ever have a problem with machines that don't have a ground, until you connect to another machine.
I have a lot of PCs in wood cases (no ground plane) and PCs running off inverters (in cars) that have no ground.
The problem there is if you plug the "sound out" into a dash radio. You get a 60 hz hum that will rattle the windows. The fix is to ground the PC to the car. If you use a set of PC speakers plugged into the inverter it works fine.
