Yes and no, I'll explain.
You cannot just grab a fade handle on an Audio Part to fade clips inside of it. You would instead double click the Audio Part and perform those edits in the editor. However, the actions "Fade in To Cursor" and "Fade Out From Cursor" (they are unbound by default so if you want to use them go to the Keyboard Shortcuts editor and bind them to keys) will work on audio parts for that.