As demand for a product drops, companies will tend to produce less of it. Whether a single person is likely to cause less meat to be produced I do not know, but the question refers to "vegetarianism" in general, not a single vegetarian. There is little doubt that vegetarianism in general causes demand for meat to drop. This is true even if not everybody is vegetarian. Thinking that vegetarianism does not decrease demand for meat, and hence the amount of animals killed, is kind of crazy.
Essentially when a person switches from a regular diet to a vegetarian diet, they are not consuming meet and therefore, less animals are killed. Economically, this is fact. However, given the population of the world, one person switching to a vegetarian diet, literally makes no difference at all. Especially when you consider the fact that most all of our food is prepared, far before we ever purchase it.
Vegetarianism does not mean that less meat is consumed and thus less animals are killed. This is because of the fact that other animal products are consumed, and then the meat is used for human consumption. Animals are used for dairy, eggs, and other parts are used for products. Vegetarianism doesn't stop this.
Currently vegetariansm is not saving the lives of animals. There have always been vegetarians and that has not stopped everyone else from eating and killing animals. If a large enough number of people changed to vegetarianism it may make a difference but as it stands right now there is no real difference.
Vegetarianism means that the same amount of meat is still going to get produced but now it is in vain and for no reason. People do not pay attention to a few less consumers, those same animals will still get killed and still get eaten by someone just not by you.
There are far too many people in the world right now that are considered carnivors for it to really make a huge difference in the amount of animals that are killed to feed our needs. Not to mention, hunting. There a millions of people out there who hunts and look at is a sport.
Vegetarianism is a personal choice people make to abstain from animal products. On the small scale, this reduces individual usage of animal products and could lead to less 'death'. However, on a larger scale we need to consider that a lot of animal procreation and popularion is controlled by food makers as well. There may be less death, but there would be less life as well.
Vegetarianism has very little impact against the number of animals killed. Not all animals killed are done so for meat, as many are killed in research, or for manufacturing (glue, furniture, etc.). Vegetarianism is also not widely practiced, and may not put a very large dent in the revenue from meat production.