No, it is essential there is some DC there otherwise the sudden changes in current that cause the noise cannot exist.
What you have to remember is that a potentiometer, no matter how bad it is, does not create noise by itself, it is currents from the signals, coupling capacitor leakage and any intentional DC that cause it. Essentially, the voltage caused sudden changes in resistance is made evident within the audio range and that's what we hear as crackle.
Note that it would be advisable to do your test twice, once with each end of the track grounded as the increasing resistance as the control is 'turned up' will result in less current and therefore less obvious noise.
Unless a potentiometer has been physically damaged or had enough current through it to burn the track, my experience is that most of the noise doesn't come from the wiper to carbon track contact, it comes from the metal to metal contact to the center pin.
Brian.