As I read this my thought was to build a cabinet out of plywood that could hold the generator and be secured to deck. With this approach you could add some sound proofing insulation on the inside to keep the noise down. Would just need I think to design it so the engine gets enough ventilation and does not get too hot. I don't see why it would not work since my diesel is closed up inside the boat in a pretty small space. Could even get fancy and maybe build a small fan into the box that will pull exhaust fumes out and direct them away from the boat. A plywood box glassed together would be pretty simple to make and do pretty far in protecting the generator from the elements. I plan on taking a long cruise on my 29 footer and your idea has spawned some ideas for me about how to stow a small generator.
You will regret the things you did not do, more than the things you did.
Get out there!
Saco Bay, Maine
2001 Beneteau Oceanis 361