>>1459195As someone who invests a decent amount of time in lifting, I can say it makes a big difference. The most common things to work on being your core, lats and obviously legs. Having a better squat will help in the sprints but won't do a whole lot else. A strong core helps keep you stable out of the saddle. And the lats help when your over the bars really mashing your pedals.
Also, people saying that working out will increase your weight don't understand the basics of exercise. Diet affects your weight, not training. Having a stronger more stable core and better mobility will not make you heavier.