I want to know if it would be possible to put an air horn on a 2014 Impala? What problems may arise?
Sure, no problem. You’ll need an electric air compressor to run the horn as well as space to mount things.
But it won’t really affect anything else.
Is this even legal, in your specific area?
How could an air horn be legal on a truck and not on a car?
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Yup. Parts stores sell kits for this, complete with a little electrically operated compressor. The only risks are if you screw up the wiring (hard to do, since they operate off of the OEM horn circuit), or if you cause a road rage incident. 
Here’s a simple to install unit and very reasonably priced! While it’s targeted for MC use, it should work very well tucked into the grill area of a car.
Note the 20 amp draw. The horn fuse might be 15 amp.
The country I grew up in . . . air horns were NOT legal on cars
In fact, I knew people that got ticketed
Crazy, wonder what the chances are you would actually get a ticket?
I worked for one company that was too cheap to put air horns on their city tractors. There were big old sprawling plants on the bad side of town that had shipping and receiving doors in various locations that you drove completely into the plan through. Because they did not want anyone from the neighborhood in the plant there were no pedestrian doors there. When I pulled up to one of those doors and pressed my little electric beep beep horn, no one in the plant would open the door. I would have to back out of the driveway and find a working pay phone to call my company and spend a lot of time explaining the problem and exact location and then go back. Saving money on those air horns cost that company a lot of money.