I'm not sure what "properly configured" means but ES has huge array of options for search which something simple like MATCH (title,body) AGAINST ('database' IN NATURAL LANGUAGE MODE) can't even begin to coming close to cover. Look at their docs, there are literally hundreds of options, dozens of search modes, dozens of analyzers and filters, scoring configurations, and so on and so forth. I am not familiar specifically with Postgres but I highly doubt Postgres supports all that or even a serious part of that - at least natively.

What I see at your zombodb link is just a way to make Postgres proxy requests to ES - complete with ES syntax and/or Query DSL. The only difference is that instead of connecting to ES directly you connect to Postgres and then add "SELECT" thing in front of your ES Query DSL. If it makes something easier, fine, but it's not "Postgres full text over ES".