Taking off the chip from Arduino
Yes and no. 

To elaborate, the sketch you downloaded to the chip has been flashed to internal non-volatile memory. So if you were to move it to another Arduino board or other device with the appropriate support hardware, then it should work just fine.

However, if you're intending to directly hook-up speakers to it and a power source, then I highly doubt it's going to work. You really need some support hardware for the chip (such as an external clock - though I think the Atmega328 has an internal clock, decoupling capacitors, amplifiers for the spearkers, etc.).