I don't think so. Some route the wastegate pressure directly out to the atmosphere through a small silencer in place of the internal passage. That might also be the source of the noise.
Or, if it's a modded street car, it could be a "pop-off" valve that vents the intake charge directly to the atmosphere. Of course that wouldn't be good if it had fuel in it already.
Ours wastegate opens a route from the exhaust manifold to the pipe around the turbo housing. That's why you can't hear it.
You could cut up a housing and add the external dump if there is room.
Or, you could plug the wastegate and add a popoff valve.