I think that an inverter is a bit like a double insulated device and does not need an earth.
We need a real sparkie to pipe in here but my understanding is that and earth is a means by which to ensure your ELCB works or prevents metal chassis from staying live as they blow the fuse or circuit braker before anyone can get hurt. Otherwise an earth is just an extra connection to which you can hook yourself up to when you are holding an active in your hand (knowingly or not.)

