Possible. Maybe he’ll get better at it if he hears the rooster enough.
We have wrens and a small meadowlark breed, but no mockers, thank goodness. There were enough of them in Henderson to make me swear off of them for life.
There are quite a few other birds (mourning doves and owls, to name two) but I haven’t seen them to put a name to their songs. Crows, of course and a couple of hawks and falcons. But I don’t know the song birds. I just like listening to them. They always tell me when the rain is going to let up.