Maybe you have to define "musician" before answering this question, but ...
Of course it's very possible to play and even create new music without the theory, and even become a successful artist. You go by what you hear around you, by what feels right to your ears and by imitating other people. It's been done since rhythm and music was invented, passing down songs by learning from others, and just playing what sounds good to you. Music theory is a very useful thing to have but people can and do make good music without it.
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On the flip side you're sometimes surprised how much formal training and knowledge of theory that some artists that play "simple rock" actually have.
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