Grand_Marlin,
Sorry to read that someone 'burst your bubble' re the perpetual thing. I personally like the idea !
FNQ, inverter in glass boat - a little dificult to connect the earth stake (especially on a high tide).
I'd be guessing that if the inverter is in a ventilated, dry (that could be difficult) location it should be OK.
Appliances that are double insulated should be no prob without earth, others I would be wary of using on a boat BUT ensure that the earth pin suppling the appliance is indeed connected to chassis. I would'nt connect the chassis to -ve battery supply since if it needed to be it would already be (internally). If not connected already it it do'nt need to be.
I think your main cocern would be to make sure the battery supply cables to the inverter can handle the current & the some, also make sure the connections to the battery and the inverter are secure & tight.(I like to spray DC connections with a "battery terminal coating" which ensures the connections stay dry & helps them stay tight .
Hope that helps
Frank