No, Haynes King is not the Panthers' starting QB. He's an undrafted rookie behind Bryce Young (starter) and Kenny Pickett (backup) on the depth chart — firmly QB3 (from the Haynes King page).
That said, he did turn heads in the Hall of Fame Game, going 21-of-34 for 180 yards with 2 passing TDs and a game-winning 5-yard rushing TD as time expired. He's getting lots of preseason run (there are four preseason games this year), and head coach Dave Canales has praised his "pro mentality" — but it would likely take multiple injuries for him to see regular-season action.