I think an age-11 Harry, facing a Sorting Hat, would probably consider himself to be ambitious and to value the trait, because he’s known little else. He might even ask the Sorting Hat to put him in Slytherin, knowing that’s what Norman would prefer. But as Dumbledore once said, the Sorting Hat probably sorts too soon…
(Though I do think Harry has an ambitious streak, it’s just more along the lines of “I’m gonna put effort into making sure my friends/family get these things’ rather than
“I’m gonna put effort into making sure I get these things”)
