Is training necessary? I don't think so. If you have an idea in your head and you know how to notate it, I think you could be a fairly effective composer. After all, we all know what good music sounds to us. Still, I believe having at least basic knowledge in theory would speed up the process of writing down music, coming up with ideas and getting past writer's blocks, harmonization, etc.
Honestly, though, I barely have any knowledge or training myself, but we all start somewhere and I'm self-studying to be a better composer.