All I can say is try it in the driveway and see how loud and how hot it gets. In my opinion the CO getting outside and into the TT is almost a non-issue. But I would just buy a $30 CO detector at Home Depot and set it on the table next to my pillow in case of the unlikely event of the CO getting onto the trailer.
As far as CO leaking into the truck cab, that's a real non issue. When you're getting ready to leave in the morning, unlock the truck cap door. Hold your breath, reach in and shut off the generator. Then go unlock and open the doors of the truck and let it air out. (for extra measure set your CO detector on the front seat after opening the doors.
If you're super concerned start the truck and turn the vent fan on high and make sure it's set to pull outside air. You can also drive with the windows open for a mile or two if it concerns you.
That's what I would do at least.