Putting any non-ferrous metal in the magnetic field of an inductor will lower its value. This is one way of making variable inductors by moving the metal. If your metal is in a low magnetic field area (in the radial direction) and not a high magnetic field area (in the axial direction) it should have little effect.
Another factor is the orientation of the external metal. Being edge on to the field will have less effect than being normal to the field.