Can yeast produce a gas when no sugar or other food is available?

If there is nothing to metabolize, which is what yeast are doing with sugar, then they will most likely not grow and not produce any CO2. With that said, there are many strains that can continue to grow and reproduce with other chemical sources, not all of which create CO2 as a bi-product. That is to say, that sugar is not the only thing they can "eat."