Does lift coefficient vary with the wind velocity for a given angle of attack?
Yes, it does vary slightly due to viscous effects.

In inviscid flow, the flow speed would not affect the lift coefficient - angle of attack relation. However, increasing the flow speed will result in a thinner boundary layer and a slightly different shape of the airfoil - boundary layer combination as "seen" by the outer flow. This influence is captured by the Reynolds number. See below for a plot of the venerable NACA 4412 from Abbott and Doenhoffs collection of airfoil data (picture source):



Note that the lift coefficient is plotted for Reynolds numbers R of 3, 6 and 9 million.