Here is the official wording from the manual...
"The generator is a potential source of electrical shock if misused. Do
not expose the generator to moisture, rain or snow. Do not let the
generator get wet, and do not operate it with wet hands."
I've run my Honda 3000i in a small drizzle a couple of times, but it's a different design than the 2000i... My manual says the same thing as above..
I would not run it in a steady rain or downpour that's for sure.
You could always put it under a canopy if it's raining too? If the wind picks up, well.... That's your call too.. :)
Good luck!
Mitch