If it does not, then there is not much reason to get a second rank, because most of the animals that would aid you with the second rank, would likely already attack with the first rank, as they would naturally be hostile to it.
Animals Respawn, so most of the ones that you killed while not having the Perk would come back, and by getting Level 1 you would stop killing most of the animals.
Besides, when a Bighorner comes and tramples a foe in front of you, it is quite satisfying.
And, come to think of it, I do remember Dogs helping me in one fight, but I think they were generic ones, not owned.