I don't think that it is the air that is degrading the grease (as in oxidation) but it is simply a matter of the more volatile petrochemicals evaporating out of the grease itself to leave only the waxy binder behind. It takes decades for this to happen, and only because enough fresh air is exposed to accept it all. It's a very slow process and can't happen in a sealed container. The oils themselves are very chemically stable as grease is designed to last a long time under conditions that are far harsher than typically experienced in a bicycle. Veggie oils can oxidize (go rancid) much easier and quicker but the oils in grease are designed to not oxidize like this for many, many years.

Most likely the only thing that may happen with grease is that it might seperate like you said. The oils and waxes are no longer in suspension. You might be able to mix it back up but grease is inexpensive -why bother? I buy it in in the 16oz tub for $5 at the local autoparts store. I like the Castrol NLGI #2 silicon-based grease because it is cheap and works well. I also like the way it smells