Jetpipe,
A headwind will increase your climb gradient. A tailwind will decrease your climb gradient.
If you agree with the above, then you must agree that we use GS. Since GS is TAS corrected for head/tail wind.
I think the confusion is in your understanding of the term "climb gradient". In your first post, you correctly defined "climb gradient" when you were defining "geometric flight path".
Definition of Climb Gradient:
The rate, expressed as a percentage, of the change in geometric height divided by the horizontal distance traveled in a given time.
Regards.