Is Jack anxious to be Auggie's friend?

No, Jack is not anxious to be Auggie's friend. He does as he asked, and he helps Auggie maneuver his new school, but he doesn't do it to befriend him, he does it because he's been asked to. Over time, however, their relationship becomes one of friendship. Jack learns to like Auggie for who he is.... not who he perceives him to be.