No, that sort of logic would work if it was, say, Charisma or something - some sort of feat to make a normally low-priority ability score be useful - but Constitution is useful for everyone, especially the stereotypically low-AC Barbarians.

It's the half again the normal effects that is really the thing breaking this feat. I think just forcing them to go into a rage to get the benefits is fine. It's nice because, hey, rage, but not as nice because if you want the benefits, you can't save your rage for a different opportunity.