Indeed it does, and not just for acceleration.
Since racing is on a closed course cornering speed and lean angles are vastly different than what one can achieve w/o being a hood ornament on the road.
A delicate brake touch to modulate momentum entering a high speed corner is required, light wheels and very good tires help here to maximize entry/exit speeds.
The ham-handed get gapped while the calm and smooth sail through to the next inevitable big jump after jump, after jump.......

edit: Modern aero wheels are very important at race pace. A well selected balance of weight & aerodynamics is in order for well rounded performance.

Of course this assumes a rider trained & experienced in competition, for plootering about, not so much at all. In fact virtually nil.

-Bandera