no, usually ground and shield are connected within host at the power supply.
a second connection would build a ground loop which makes the shield useless.
Well.. no you wont.
Putting one shield on top of another will improve shielding, not destroy it.
If you have two grounding path in parallel they lower the resistance and the inductance so they can only improve the grounding not worsening it.
I never understood all the fuss about avoiding ground loops, star grounding and other weird constructs.
Just provide the lowest enough inductance possible for the ground.
Inductance lowers if a wire is wide, that's why a ground plane work as a low inductance ground.
I imagine that in a large factory if would be expensive to put down enough copper to make a low inductance ground over the entire plant so you will have to live with inductance and resistance in the cables and that will in turn create ground loops between different stations spread out on the plant. In that case it makes sense to create star grounding or use optical or magnetic isolation between stations.
But on the desk, just provide the lowest possible inductance and resistance for ground, alternative path for ground in this case will be an improvement as it means you paralleled the resistance or inductance with another and that will bring the total resistance or inductance down - that is what we want!
Shielding helps avoid emitting or picking up radiation due to the antenna effect (current in a wire will radiate, radiation in to a wire will create a current).
This problem gets worse if the wire is long or if the impedance of the receiver/input end of amplifier is high impedance, that is the reson why wires are usually shielded - they are long.