I'm going to guess that they didn't equip it with a smoke detector, propane detector, or CO detector....if ALL you have in the GN is the AC, add in a smoke detector and a CO detector (mount it low, that's a heavy, low gas) and I think you would be fine.
If the A/C requires the engine to be idling there could be a carbon monoxide issue. I read not too long ago about people who died of CO poisoning because of running the engine to power something, cannot remember now what it was, probably a heater.
RIP Sasha, best dog ever, pictured shortly before she died, Death either by euthanasia or natural causes is only the end of the animal inhabiting its body; I believe the spirit lives on.
The A/C doesn't need the engine, but it does need a 110V power source. Most LQs have a kick out window in the GN for emergencies too. You can change that out pretty easily and then mount your detectors.
If you've got an A/C you're on your way, but are the walls and roof insulated? If not the A/C is going to run like the Devil trying to keep the area cool. Do you have any windows? If not, it can get kind of claustraphobic. Does it have a vent? If not it's going to get "close" (even with the A/C). I would find an unfinished gooseneck area unsatisfactory as a sleeping quarters, but YMMV.
We had a finished tack room and mid tack area that we combined and made into a "weekender" type area. We've got windows, a bar sink, 'fridge, microwave, and Incinolet. It didn't cost all that much (way less than a formal LQ) and is good enough that we've spent as long as 14 days in it.
To run the A/C you'll need 110v power. That means a hook-up or a generator. If you go the generator route I'd recommend a pair of the Honda EU-2000 gensets hooked in parallel (giving 4000 watts of capacity). They are not cheap but they have a three year warranty and run very quietly. They can also be easily loaded and unloaded from a pickup by one person. Finish the system with an extended run time tank and you're in business.
What the warning means is that the laywers that work for the company had to do something to protect the company should someone sleep in the gooseneck and die... people have slept in goosenecks for ages, and I've never heard of anyone dieing.