Some of the Avengers would be very protective. Captain America would see Harry as a kid in need of guidance and safety, just like he does with his teammates. Tony Stark might be initially skeptical but would soon see the potential in Harry's magic. Thor would probably be fascinated by Harry's magical powers and see him as a worthy addition to their group.
Sakura would probably be a bit skeptical at first. She'd worry about how Naruto could take care of another person when he's always so busy with his ninja duties. But once she sees how much Koneko needs a home and how Naruto is committed, she'd warm up to the idea. Sasuke might not show much emotion on the surface, but secretly he'd respect Naruto's decision. Shikamaru would think it's a troublesome situation but would also see the good in Naruto giving Koneko a chance at a better life.