B. wrote:
"Is the coax shield "always" tied directly to the radio chassis ground,
(which is also earth ground for my set)?"

"Always" may embrace too much. Usually, the coax shield is almost
directly connected to the radio chassis ground.

B already implied that his dipole has a potential problem as its
connection to the grounded inner surface of the coax shield is shared at
this point by connection to the outer surface of the same coax shield.
This inherently unbalnces the load on the inner surfaces of the coax.
The center conductor has only one load, its half of the dipole. The
inner surface of the coax shield has two loads, its half of the dipole
and the outer surface of the coax.. This is fixed by by a balun between
the balanced dipole and the unbalanced coax.

On the other hand, you may have no objection to distortion of the
dipole`s pattern by radiation from the coax exterior. In some cases it
won`t hurt. In other cases it may be beneficial. It is somewhat
unpredictable, but many dipoles are directly fed by coax and are
satisfactory.

Best regards, Richard Harrison, KB5WZI