I have a Honda 2200i and a soft start on my 16k btu AC unit. I use it (and bring it) only very rarely, and then I have it aft in the cockpit with the seat lowered and the exhaust blowing out over the stern, downwind. I have Carbon Monoxide detectors throughout the boat, and test them/replace them regularly. None have ever alarmed with the Honda running on deck and the boat closed up. It can be finicky to start the AC unit, but eventually works. It will run all night on a 5 gal tank with fuel to spare, but NOT on Eco mode. I've considered converting it to propane, to keep gasoline off the boat, but the efficiency isn't any better, and getting propane refills at fuel docks is almost impossible - whereas gasoline is readily available.
But I've found that there are two issues that give me pause to bring the generator and use it - even though our Chesapeake summers can be exhaustingly humid and hot - even in the evenings:
1. Storing gasoline/gasoline filled generator. There's nowhere below deck to safely store either the external tank, or the generator with fuel in it. Lots of people do put the generators below - one poster mentioned under the nav table. Your boat your choices skipper, but there's gasoline in that generator and a risk of leaks and explosion. On my boat the battery switch is under the nav table, as is the shore charger, and I'm concerned about fuel vapor and a spark. I just got the generator back from a Honda recall that supposedly fixed a potential fuel line leak at the fuel valve, so the potential is real - not just me being over cautious. If your boat burned to the waterline, and the investigation showed gasoline or a gasoline generator stored below decks was responsible, I'm gonna go out on a limb and say that insurance may have a big out when deciding whether to pay the claim. I don't know that for a fact, but I do know insurance companies. I have stored the Honda in the aft locker on deck, but it is not vented nor is it really separate from the interior of the boat in any vapor or waterproof sense, so I've taken to storing it on deck. The 5 gal tank fits nicely and securely under the helm seat on deck. Still, I worry about corrosion on the Honda being stored outside around brackish/salt water. Another recall for these generators was because if they're around salt water they can corrode, then smoke and catch fire. If you're using your Honda generator like we're talking about PLEASE make sure you've gotten it in for BOTH of these recalls, if its affected. And bear in mind, for many reasons, Honda does not officially condone these generators for marine use - and the recalls demonstrate why.
2. Noise - in two parts. My boat is 36' long, with cabins fore and aft. If I run the generator on the aft deck it really transmits significant noise and vibration through the boat such that sleeping with it running is a mixed blessing - the AC runs nicely, but its loud enough to make sleeping through it difficult. No way my wife could do it. I can manage it, but its an issue. Its much more of an issue in the aft cabin though. In the forward cabin I can barely hear it, so that's my preferred place to sleep if its running. But the other part of the noise problem is for everyone else in the anchorage. Yup, I get it, those little Hondas are about as quiet as generators get. But its not quiet enough to keep from bothering your neighbors, who may be sleeping with their screen-covered hatches open, hoping for a quiet night on the water. I've ONLY used it when I'm alone in an anchorage. I would be peeved if the guy next to me ran the thing while I was trying to sleep with the hatches open. I've read about some extreme efforts to quiet them - put them in a dinghy with an insulated housing, etc., but that just seems a ridiculous amount of effort.
For the most part if I'm out in the hottest part of the summer overnight, and it seems like sleeping will be awful, I just get a slip and eat the cost. Especially if the wife is with me. I've tried everything else - hatch scoops, fans, sleeping on deck (mosquitos), etc. Those definitely help in some circumstances - not so much in others. Some nights you just have to have AC. I have looked into a small, permanently installed generator to run my AC, but for the $15,000=$20,000 it would cost new and to install it, I can book a LOT of nights in marinas and come out WAY ahead. I might think differently if I was cruising full time, but for mostly weekend fun with a few longer trips thrown in, it doesn't make fiscal sense for me.
Your sailing situation may differ, and I wouldn't seek to impose my circumstances and solution on anyone else, but that's how I thought through and experimented with this problem over time.