Music from a laptop- on AC or via battery power?

I see that in the digital world, linear power supplies are often touted as offering a lower noise environment. 

Suppose I am using a laptop. If I’m running it off the AC, certainly the switch mode power supply is in action. Am I correct in thinking that if I’m running strictly on battery power that the power supply is at lest as clean as an active linear power supply? Or is there sill a switch mode power supply still actively doing its thing in the laptop?