It is not entirely that simple. Condensate water is potential problem if wrongly discharged. But adding sufficient drainage is not that expensive per balcony basis. So it is something that should be fixed.
There are also systems that spray the water back at the AC unit to cool it down, this is supposed to both improve efficiency and evaporate the water so you don't have to deal with it. I am sure those have some downsides, too.
And with spraying it on ac you want complete evaporation or you are back to same problem.
As said it is not too hard problem but still something that most likely requires consideration.
Sure thing, you could go to court if they have any problem, but who is going to fight for AC worth $500 for a few years just to get it installed?
Best would probably be to use the existing rainwater pipes that lead down to the sewers - all building have those. But good luck getting that past your HOA-equivalent, as that will most probably involve some modifications to the building and we can't have that, no!
edit: I guess you could route the drain pipe anywhere if you wanted, so I retract my previous statement.