The kickdown cable on your 350 has only one function, enabling a forced downshift when the throttle is pushed to the floor. It's also called "passing gear" by some folks. The shift points are controlled by the modulator, which varies pressures according to manifold vacuum.

On some transmissions the kickdown cable is also the throttle pressure control, and must be adjusted to a very precise position for proper functioning of the transmission. Ditto for throttle linkage on the Powerglide, and the Dual Range Hydramatic. On the TH-350, it's only for a forced downshift.
Jerry

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