Tom,

Many configurations of the type you describe are widely misunderstood.

To help you to analyse the configuration, keep in mind that for a coaxial
cable in TEM mode, the current flowing on the outside surface of the inner
conductor is accompanied by an equal magnitude but opposite phase current
flowing on the inside surface of the outer conductor.

Consider a break in the sheild as a circuit node with at least two
connections, the inside surface of the outer conductor and the outside
surface of the outer conductor.

The configuration you describe will make essentially no difference to the
common mode current, the feedline is not effectively shielded by the outer
conductors.

Owen