UC A-G requirement

If one takes the AP Music Theory course without taking the AP exam, will it still satisfy the visual and performing arts A-G requirement for UC school admissions?

Yes, as long as the AP Music Theory course is a one-year long course or offered over two semesters. You do not need to take the AP exam as well.

Alternativelty you can take an AP exam only and score the following:
Score of 3, 4 or 5 on the AP History of Art, Studio Art or Music Theory Exam;
score of 5, 6 or 7 on any one IB HL exam in Dance, Film, Music, Theatre Arts or Visual Arts
http://admission.universityofcalifornia.edu/freshman/requirements/a-g-requirements/index.html