Would yeast be alive or if you add it to a bottle of ginger ale?

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.