Not only can she, she does attack all the time. She distracted the other Siren while singing other defensive melodies, but her attack never stopped, even when she got hit. San is capable of singing two songs at once.

She doesn't talk because she's holding back, per the lolicon karate club president. There's no mention of strain on her vocal cords. The official rumor was that she was abandoned by her parents because they couldn't handle her full powers. She's a magnitude stronger than the average siren, as we witnessed during the beach arc.