It more common to come home to a hot house with a broken AC while leaving the system run with no one home. On the flip side it's probably just as common to come home and find everything is fine. Albeit in your case the upstairs will be a little cooler than the rest of the house.

There is also the slight chance you come home to a caved in ceiling, depending where the system is located. If you live in a humid climate the AC is capable of making upwards of 5 gallons of condensate an hour. When your system is installed and designed with these sorts of things in mind there are controls to shut the system off in an event like this.

PS: I am still to this day (2017) without a properly functioning crystal ball... even though this market could cause me an early retirement. I must admit it would be rather difficult to read palms from a forum board. Oh, the humanity.......

This could also happen.....

Have a nice trip....

It is not going to cause damage or a fire. Most of the cool air the down stairs AC generates stays on the lower floor. The upstairs AC will be operating a little more than it normally would, but not enough to cause any concern.

agree with Mike...depending on outside conditions, the hot unconditioned air from lower floor will rise and impact the 2nd floor system making it work longer.

IMO

Injoy your vacation,it is no more likely to catch fire while you are away than at night while you sleep. If mine decide's to catch fire I'd rather not be home anyway,

Is there no one else that turned a window A/C on in June and left it running almost continuously until end of August?

It is not going to cause damage or a fire.

Fire is rather unlikely. I sometimes get upwards of 2 calls a year in which the ceiling caved in... some times it's the AC, other times it's the water heater.

Depends on what you consider 'damage'.