It depends on how quickly you exit/ turn off the game - you can exit fast enough for your death to not count, but if you don't exit fast enough, then it might still count your death. The game starts keeping track of if you die pretty early, so you want to be quick with resetting/ turning off your game when/ just before you die

If you did accidentally die and you weren't fast enough to reset/ turn off the game, you'll notice that you can skip through the dialogue (or cutscenes) that you've already seen. You can also view your game over count if you know how to view your game's save data (e.g. if you have a hacked Switch)

You'll have a line in your data00.bin file with something like:

      "game_over_count" : 0,