I don't KNOW the answer to this but my guess is - No.
I THINK only special attacks that have some sort of elemental wave with it (for example, if you see fire in Ares' sword attacks, they include SOME elemental damage or Hades Sword's 3 quick slice special has purple streams with it).
The Gladiator Sword I don't think uses elemental damage at all. Someone who knows or who has tested tis more should answer though lol
^Evidently Im a bigger gow nerd which god do you primarily use sir?
Right now I am level 24 Hades, gonna max him out then try to max his equipment BUT I had a TON of fun using Poseidon, though I will eventually settle on Ares, my Allegiance of choice.
I'm rolling a 100% Hades Healer right now lol Full Phobos gear though...But man Zeus needs 3 Lightning Storms to take me down at least and most specials barely **bleep** my armor
Also...That Lance is awesome...