If you’re watching something from the 70s, sure. I would hope synthesized grain isn’t being used in this case. But for anything modern, the film grain was like

If you’re watching something from the 70s, sure. I would hope synthesized grain isn’t being used in this case. But for anything modern, the film grain was likely added during post-production. So it really is just random noise, and there’s no reason it can’t be recreated (much more efficiently) on the client-side.