The logic behind it is so simple, the higher the tide the less room to move for the wind, the faster it has to travel (same volume).
Sorry, but this logic is incorrect. Reducing the volume (really cross-sectional area) of any passage, whether it's a hose, river, tunnel, valley or whatever, will slow down a fluid passing through if a constant pressure is acting against it, which is the opposite of what you are suggesting. The exception to this would be a very specific local constriction which could create a local venturi effect, but this would not be created by tide.
Regardless, the effect of this is utterly insignificant and I could present a dozen other principles which are just as important but still insignificant in the context of tide.
But I can immediately think of two factors that may have a measurable impact. They are:
1. There is shear, or friction between wind and water, and just as wind drags the surface layer of water with it (and converts wind energy into waves), the tidal current will drag against the air, but only to a very small degree. Therefore, a change in the direction of current could change the wind strength and direction a little.
2. Sometimes a change in tide introduces water of a different temperature into the weather system. It may be cool ocean water, warm bay water, replacement of cold river outflow with warm, or any number of other local possibilities. Even a small temperature change of the water surface where you are, or even many miles away, could have a significant effect on the wind where you are.