If I properly understand what you're asking, yes, it seems to exist outside of the DRK's head.
This was likely Darkside, which Fray explains is similar to magic while warning that energy sourced from dark emotions can consume you:Originally Posted by Ishgardian Citizen
Originally Posted by Fray
To go off on a digression...
The mythology states that Hydaelyn and Zodiark once shared the aetherial sea; Darkness (capital D) seems every bit as aetherial as Light, down to the existence of Darkness crystal and Darkness sprites. Just like Paladins and White Mages can harness aether in ways that that seem to tilt towards the Light, it seems as though the Dark Knights can do the same in the opposite direction.
However: the darkness mentioned in reference to Dark Knight is lower-case. It seems to be a poetic darkness within. Does the fact that we still see Darkness auras and Darkness sprites and Darkness-based abilities hint at a Darkness within (a la Promathia and Final Fantasy XI)? We can only speculate, as we have been for a long time. (Thanks, Ramuh.) Thankfully, it doesn't seem as though your query requires going quite that deep!
To the contrary, NPCs (such as the Moogles) don't seem to believe that Dark Knights do much more than harness their own emotions (as Fray hints at right off the bat). They are allowing the pain and anger that is born when justice and love are abused to become a furious and tainted source of energy. Even Sidurgu comes around to believing that these dark emotions arise from desire to protect that which we hold dear. The "flame in the abyss" of which his master spoke is that very passion. The fact that he was using Rielle as an excuse take revenge on Temple Knights for murdering his family blinded him to the role that his affections (for both his family and the girl) were playing in his harnessing of that darkness. Again, it doesn't seem much different than a Paladin's energies manifesting as if they tilt towards the Light.
Perhaps, as in all things, man cannot invite Light into his heart without it casting a shadow.