Yes, he could play in it. In fact, he played in a similar system in the early "big three" era, where he was the primary ball-handler, but everyone touched the ball a lot more. Rondo's role increased over time, to the point where he became ball-dominant. However, it wasn't always that way.
I don't think he'd be as effective as Parker with the Spurs, though. Rondo is inferior at scoring, penetration, shooting, and FT shooting. Rondo is probably a better / more creative passer, but I think Parker is probably better (if for no reason other than familiarity) in terms of initiating the Spurs' offense / making quick passes that don't always immediately lead to open shots, but that do facilitate the offense for others.