No, Arrow came out in 2012, Flash and Constantine in 2014 (with Flash debuting a couple weeks first), though Barry Allen made his debut in Arrow before getting his own show. So Barry and then Flash predate Constantine.
Even then, Constantine was to be its own show separate from the Arrowverse (similar to CBS' original intentions with Supergirl), but the discussion of incorporating it into the Arrowverse came partway through the season, and only made an actual reality in Arrow's fourth season. And only then was Constantine retroactively made a part of the Arrowverse. The trick is that Flash and Legends are spinoffs of Arrow, but Constantine -- even though it was retroactively absorbed -- is not a spinoff of Arrow.