No. Wrong. Privilege implies no such thing. Privilege is not a moral judgment: it is a description of a condition. You are privileged when you have advantages due to your religion, birth class, sexual orientation, or other socially relevant criteria.

You are a dick when you refuse to recognize when you are privileged and act to reinforce your privileged position.

Pride (or shame) in other people's actions seems irrational to me (unless you had some involvement).

Why should I feel proud that I am from the same country as Isaac Newton? Or shame about the bombing of Dresden? I had nothing to do with either of those things.