Coming back to this from a few days later, the search "Dr. Paul Drago" doesn't turn up anything negative in the first dozen pages. Unfortunately for him the search bar is offering up "dr. paul drago domestic violence" and "dr. paul drago botched" as auto-complete options.

I think so, at least to some degree. Someone's certainly bet money on the theory that it works.

When I first saw this tweet, a search for "Dr. Paul Drago" (in an incognito window) consistently returned a glowing blog post first and the domestic violence article second. Hours later, those results are consistently reversed. Could be random, could be that people who saw this tweet are intentionally clicking the news article he's trying to bury.

or could be google took manual action

If you search for the requested terms, most of the top links are spam blogs and other junk sites that describe him in glowing terms. It appears that they've successfully pushed most but not all of the critical articles down to the second or third page.

You're putting a bit too much faith on Google algorithm, then again maybe the whole world is.

Based on the current results, I'd say it works very effectively. It's almost impossible to find the article about the 11 botched surgeries.

My guess is that it could work. It would be hard to detect, because the queries come from real users.