Yes, the more people who commit to vegetarianism, the fewer animals will be raised and slaughtered. It's a group effort, but it takes individuals like you, one by one, to make a difference.
I work in a restaurant. We have lentil burgers and beef burgers. We sell more beef burgers than lentil burgers. But if more individuals ordered the lentils instead of the beef, we would order less beef. Therefore, our supplier (or grocery store, wherever) would have extra meat that did not get sold. It would go bad. So they would not order as much next time. Then, say, the butcher wouldn't butcher as many cows, so the rancher would have a few left over.
So, you see, this would take time, and some meat would get wasted, but it would definately pay off in the long run for you physically and for the planet.
I would strongly urge you to either become vegetarian or cut back to almost no meat; and, if you must have meat, get it free-range, grass-fed, and locally if possible. It's more expensive (which means you won't feel like you need to buy it that often) tastes way better, and you can have the peace of mind that you're eating a happy cow, not one factory-raised. Same goes for poultry, eggs, etc.
If individuals like you are enlightened in this area, we can make this world a happier, healthier place!