I would not worry about a AC unit. Now a new deck, or a new shed or shop building and no permit will raise some flags.
As for getting the permit, at least in my area, get them. It can save you heart aches down the road. I know a guy that built a shed in his backyard, not permit and it was obviously not to code. Can you say tar paper shack? It was also easily seen from a busy street. Someone complained and the city came out to take a look. Today the shed is gone and so is the unpermitted wood burner in his shop. I don't know what else the found, but around here the inspectors get nasty when they find unpermitted work, at least larger stuff and tend to look over the whole property with a fine tooth comb.
Why contractors don't get permits? So they can get the job done faster and no worry about a code issues. I would not hire a contractor that did not get a permit. Depending on the area the inspectors can be tough. I worked in HVAC for years and the inspector was very tough and by the book, he was also fair and easy to work with if you did things correctly. Now on the other side companies that were hacks didn't last long, or they cleaned up there act. It leveled the playing field for contractors because the job had to at least meet codes where where there is no inspections anything goes. After I got out of the field I worked as an route salesman for an HVAC supply. Traveling out in the country where there was no inspections was scary. I have actually seen stuff so poorly done by more than one of my customers I told him to clean up their act or don't take me into their jobs because I didn't want to see it and assume any responsibility for it.
I built a deck on the back of my house. The city provides a code book in regards to decks to homeowners at no charge. When I got done I called the inspector and he stopped by for a look. He spent about 10 minutes looking it over, even crawled underneath to check the framing. He smiled and said "Nice job!" and signed off. He went on to tell me how many times homeowners get a permit, they get a copy of the deck building codes and still half as it.
I like inspectors and building codes as long as the inspections follows the codes and just doesn't collect the fees and never inspect.