Having a chip on your shoulder being from a non-target is OK

Everyone hates those non-target guys who have a chip on their shoulders. Why? Because they're assholes. That is, they project their anger onto others. This behavior is not ok.

However, if you if you fall into this subset while being a good person, then I would argue it's OK. If it energizes you and drives you to do more, then I would argue it's GREAT. Just don't be a dick. 

Tom Brady was a 6th round draft pick who no one really believed in early on in his career. He said it drove him at every step of his career while still being a great teammate and leader. Be like Tom Brady.