Embedded System on Chip= ARM cores + Peripheral(SDIO, USB, I2C..) Controllers + Video/Audio Decoder + Interrupt Controller + Power Manager Unit Controller + RTC + ...
Most of the SoCs are designed to have different power rails to all ( or few combinations) of these modules. I am not aware of any SoC which keeps ARM core running while playing music when screen is OFF. To serve an interrupt, you don't need to keep ARM running. You can always wakeup ARM core through some custom circuitry and save power.