Yes you are encouraging the yeast to grow. The yeast also has the option to "aerobically" respire to produce energy for this purpose, but it oddly prefers the inefficient anaerobic method of producing energy (fermentation) as long as there is plenty of food about (source: probably a Whitelabs information flyer).
Their survival strategy basically involves producing CO2 because it inhibits the growth of most other microorganisms (because most others respire aerobically). But this means they themselves have to respire anaerobically. Ditto alcohol; they evolved the ability to produce alcohol (and to live in it themselves) because other microorganisms don't like it.