Not an expert, but I'd say no, no overhead. The user object is already on the client, so there is no network traffic involved. So it's either getting an object from the Meteor global, or passing an object as a prop.
It's probably more of a design philosophy question: Do you believe that your React components should be pure, pass it down as a prop. On the other hand, if you believe Meteors usersystem is an integral part of your app, and you don't want to pass too much props down every prop, call it directly. Both are fine.