You can get a long way just "by ear" , it has it's limitations, but there's a lot of gigging amateur musicians that never reach those limitations by sticking to what they know or have had time to practise.
Anyone hoping to move on to a "proffessional" stage will need a decent grounding in notation and theory.
Having said that, all the theory in the world won't help the player who doesn't have an "ear", so if it had to be a choice of one over the other, the "ear" would win every time!

Joke: Q. "How do you keep a guitarist quite?"
      A. "Put a sheet of music in front of him!"

C-flat