Whether overnight success exists depends on the definition of "success". Becoming skilled can't happen overnight, but recognition does and, since most people are not independently wealthy and have to work, recognition sadly matters a lot more than skill, practically speaking.
Growth in one's skill level is gradual and relatively steady, but the selection process for the "stars" is full of dumb luck, black swan events, ridiculous inefficiencies and, often, catastrophic failures (e.g. Mark Zuckerberg, the guy who stole the right idea from the right people in the right place at the right time).
The relationship between skill and recognition is complex. Most writers and artists who become "established" devolve into mediocre hacks, because the cocktail parties take over the time they'd otherwise be using to improve their skill. On the other hand, what happens to the vast majority is that the utter lack of recognition, despite their talent, discourages them and they move on to other things. In truth, the "star" system that has infected most aspects of American life-- business, art, academia-- is one of the worst influences on quality imaginable, and much of why the product of humanities academia is utter jenkem. The 2007-08 financial clusterfuck is a result of many individuals' efforts to become "star" traders. Bankers are not stupid people who just happened to be broadsided by a black swan; they deliberately took extreme risks (often hidden behind models known since the '80s to be flawed or incomplete) with others' money, knowing that they'd become stars on the upside.