I term China's stint with C919 and C929 as catch-up and learn phases.
The number of foreign equipment and subsystems used aboard these aircraft are massive. So much so that I'm inclined to believe that another unexplored side to this story exists - one of gauging the quality and standards required in the current Aviation market.
The real customers of Civilian Aircrafts are Airline Operators ( Etihad, Quantas,Luftanza etc). No one will choose a Chinese aircraft fitted with Chinese subsystems even if China could demonstrate better Economics. Because ultimately, there is a lack of trust/ brand awareness associated with Chinese systems. China needs to demonstrate the quality and reliability of its systems over a long period (spanning a decade or two). These aircraft are the stepping stones to that.
The various foreign subsystems are going to be gauged for their performances and attempts will be made to gradually develop competent local subsystems to replace them.
So... while Rockwell Collins may very well provide the Flight Management System for C919/C929...China will/ should make attempts to create a local answer to the RC solution.