Take it for what it's worth but I have run my 13,500 BTU air conditioner on 15 amp service on many occasions with no issues. If there is a 15 amp breaker in the line it should protect against overheated wires but not too likely to have any issues like that. Just don't leave the water heater or fridge running on electric at the same time.
Concerning the generator, do remember that they rate the DBs at a prescribed distance (like 7 feet or so) but they ALSO usually rate them with a 50% load or less so you may see higher noise if it's running harder. Just something to consider. I DOUBT if the noise from the generator would be a major issue either since others in their homes will likely ALSO have their own air conditioners going and windows mostly closed.