That is per building code for gas hot water heaters.

That's correct but if you install a fan you're now going to pull air in thru that vent and down the flue. Air travels in the path of least resistance and if the only way to get replacement air is thru that grille and flue then that's where it will take it from. I sold ventilating equipment for 40 years and I only mention this so someone doesn't unknowingly create a hazard. Make sure if you have gas appliances you have a source of replacement air.