I don’t know if it’s listed for outdoors exposed to the elements. Either way I understand the desire to protect it, but under an attached patio cover creates a risk of carbon monoxide poisoning. Then there’s a fire potential. Think of it this way, would you be comfortable if a Volkswagen was sitting there....with the engine running.
The manufacturer should have directions regarding this. As an inspector I would reject the setup. I can’t think of a code violation other than not following the manufacturer’s installation instructions.
I am never the last word on anything so it may be just fine. Kinda deadly....but just fine.