Larry Niven used that type of engine for the rocket the humans used to fight against the alien invaders in Footfall. THe Atomic Energy Commission began testing them in 1955. The Soviets also tested some too, in the late 1950’s. And perhaps after.
Why would Clarke/Kubrick be concerned with the propulsion system when they didn’t have to show it in operation–the ship is in “coasting” mode throughout the movie.
There are quite a few differences as to the Discovery and its mission between the 2001: A Space Odyssey script, Clarke’s concurrently-written book, and his later sequel 2010: Odyssey Two (adapted for the screen as 2010: The Year We Make Contact). Perhaps most importantly, the book has the Discovery taking up orbit around Japetus with no fuel left; the sequel (both book and movie) says there’s enough fuel left for Discovery to leave Io orbit to avoid “something wonderful.”
I always figured, as the Leonov dipped into Jupiter’s atmosphere for the aero-braking maneuver, it could fill up it’s fuel tanks with hydrogen with a “ram scoop”.