It would be enough to turn any boy's head. Famous before he can walk and talk! Famous for something he won't even remember! Can't you see how much better off he'll be, growing up away from all that until he's ready to take it?
(Harry Potter and the Sorcerer's Stone)
Is the participial phrase the modifier for he, or the adverbial phrase implying cause of the "how much better off he'll be"?