I am well aware that Western notation is not the only one, however, I cannot see how music theory works without any notation. Whatever form of notation you choose to encode information in will still have to be decoded, i.e. read. The reason why some notations have been more durable than others is the relative amount of information that can be stored.

Tabs for guitar and bass are just one example of a deficient mode of notation, since they cannot provide all information necessary to play something.

If you want to forego all notation, however, understanding theory becomes even harder than with a deficient notation. For that, you'd have to solely rely on somebody's ear in order to explain roots, scales and afterwards more complex topics. The only other option is teaching visually, which ist somewhat possible with a guitar, and somewhat possible with a piano, but is not transferable to another instrument afterwards.