That's only a meaningful question if the only "true Left" is a Leftist political party that is centered around some form of Socialism that controls a meaningful amount of a State.
Not necessarily. A Syndicalist or otherwise Anarchist-derivative party doesn't exist either, and no similar coalition exists on the ground with widespread impact on the Capitalist status-quo, yet.
I really hope you're not trying to insinuate that the DNC are somehow left wing.