Yes, it applies to an asynchronous generator if it's operating at or above synchronous speed and its field is excited so it acts as a generator instead of an induction motor. The mains frequency and number of poles determine the synchronous speed of the generator, so the formula applies.
In engineering circles "alternators" generally refer to the small rotary AC generators used in automotive applications. Otherwise anything that creates electricity is a generator, whether it be DC or AC. That's why large diesel-driven AC units, for instance, are called "gensets" or generator sets, not "altersets" or alternator sets.
Many people refer to the AC generators used in wind turbines as "alternators", which is not incorrect - any AC generator can be called that if you wish, as the term is ambiguous when referring to AC generators.
--
Chris
