Whether or not the parshendi or parshmen are/turn into voidbringers I am not certain, I agree with The Count that it probably isn`t as simplistic as that. I agree with the other part of your theory that the voidbringers can definitely use stormlight.
(Not sure of page, I do not have the hardback with me) Chapter: Prologue: To Kill
"Holding his breath, he clung to the Stormlight. He could still feel it leaking out. Stormlight could be held for only a short time, a few minutes at most. It leaked away, the human body too porous a container. He had heard that the Voidbringers could hold it in perfectly. But, then, did they even exist? His punishment declared that they didn’t. His honor demanded that they did."