I can't notice much of a difference to tell the truth, but as a roller I'm basically always either swimming or rolling, so yeah.
EDIT: Ok nevermind, I went back and doublecheck and it does effect your movement speed when you're firing any weapon that ISN'T A ROLLER.......which is dumb. I'm not sure if this is a bug, or intended, but the bottom line still stands.
Running speed only affects IDLE running (Just holding the L stick forward and nothing else) When you're rolling a roller, you're technically using your weapon set a static speed like all other weapons. So to answer your question, No it does not.