As per the title. Did Iron Man's grandfather have a role in the creation of Captain America?
In the comics (Earth-616), the simple answer is no. Dr Abraham Erskine created the Super Soldier Serum and that is what gave Steve Rogers his amplified abilities. No Stark is credited with the creation of Captain America.
In the films (MCU), the answer is also no, but there might be a reason why you thought so. Dr Abraham Erskine created the serum just as in the comics, but it takes more than just ingesting the serum for it to work. The subject (Steve Rogers) needed to be exposed to a specific type of radiation in conjunction to receiving the serum via injection into all his major muscle groups. To accomplish this, the SSR enlisted the help of Howard Stark, Tony Stark (Iron Man)'s father. I don't believe Howard Stark's father is ever mentioned, aside from a brief line in the show Agent Carter, when Howard Stark talks abut where he came from.