When you buy commercial yeast, it is in a dried form and the cells are in a sort of hibernation. When the dry yeast is exposed to water, the cells become re-hydrated and they resume their normal life processes, including respiration, fermentation, and reproduction.
Ginger ale is mostly water, so yeast added to it would be able to hydrate successfully and "wake up". Like all sodas, ginger ale does have carbon dioxide dissolved in it, but yeast are able to tolerate fairly high CO2 levels without harm. The limiting factor here is food. If you use regular ginger ale, which has sugar in it, the yeast will be able to use the sugar for energy and will live and reproduce. If you use diet ginger ale, which contains chemical sweeteners instead of sugar, the yeast will not have a food supply and will die off quickly.