I don't know of any source that suggests the bacteria that oxidize ammonia/nitrites have a dormant stage.
I think what you probably would see is that the bacteria could do OK without food for at least a week. After that you'd start seeing a gradual die-off of the biofilter that would probably leave you without many beneficial bacteria after a month or so.
I have aging tanks that have cycled that regularly go a week or more without any apparent loss of their ability process modest amounts (1 ppm) of ammonia. Even after two week vacations they seem capable of handling the ammonia, although I confess I haven't checked on whether any efficiency is lost over that period of time.
Jim