can i use a 700c tire (Gatorskin 700c x23) on a 650 wheel
No you will not be able to use your 700x23c tire on a 650c rim. The bead seat diameter of 700c rims is 622mm, this will also be the bead diameter of the your 700x23c tire.  The bead seat diameter of a 650c rim is 571mm (see Velocity's Spec section). Your 700x23c tire will be 51mm too wide.