Some inverters are grounded or can be grounded allowing RCD operation. (I use a 1200 Watt Selectronic sine wave inverter at my holiday home with an RCD)
Some of the cheaper inverters have one side of the AC output connected to DC ground (non isolated) and can be lethal.
This inverter for example has electrically isolated output, theoretically at least, the neutral side (if not already connected to the earth pin) could be grounded and an RCD used, you would need to firstly ascertain whether your inverter is electrically isolated, then do some tests with an RCD.
If your inverter isn't electrically isolated I wouldn't be using it out in the damp of night.
Google for using an RCD with inverter, you'll find more information.