No, it isn't true.

In August 2013, to commemorate Curiosity's first anniversary on Mars, the team responsible for the SAM (Surface Analysis at Mars) instrument, sent a command script to the resonator, that vibrates to cause samples to descend, such that the vibrations would match the Happy Birthday song. Normally the resonator tones are pretty non-distinct. Curiosity is not programmed to repeat that experience at a preset time.

If the ground chooses to repeat that procedure on some future birthday, they can. But to the best of my recall, they did not repeat it on August 5, 2014.