It's not the turbo. Your turbo is only spinning when there's a load, and you've got your foot deep into it.
What you are hearing is you Secondary Air Injection Pump. May be on it's way out, but you can hear it normally (although it's not that loud). It's an emissions only system, so it does not effect performance. It only runs when the engine is cold to flow additional air into your exhaust to more quickly heat up the cats.
So if it is going you'll get a CEL, and hear a heart stopping beep accompanied by "EMISSIONS WORKSHOP!" on your dash display, but it aint no thing but a chicken wing, so don't worry. It only an annoyance and can be delt with once you get sick of the light.