It's clearly a site penalty for most of us, yet there was a whole thread here a couple weeks ago tying to definitively state the opposite:-)
Since I don't have any thin content and never played any SEO tricks, I've got nothing to change but our simple HTML site architecture, and I'm not going to do that. I have gotten busy with DMCA complaints and filing Google spam reports, etc.
While I don't track individual search terms as a rule, I've kept up with a couple exact phrases (that nobody ever searches on) to see the results. In at least one case where my own page didn't even appear in the rankings anymore, getting the #1 result (a verbatim infringement) removed and using the public URL removal tool to report that allowed my page to reappear in the rankings, and in the #1 slot to boot.
But the loss of visibility for search phrases is just a symptom of the whole site being penalized so that unauthorized duplicates are now seen as more authoritative, even those on article farms. Whether the massive infringements and unauthorized syndication over the years are responsible for the site penalty, only Google knows.
And getting back that #1 slot has zero impact on the traffic for that page. Getting the duplicate removed didn't increase the trust rating for the original, it just got rid of the squatter that had taken its place.