Chad and Ryan don't interact at all in the first movie, but interact in the second movie. There's tension between them at the start of the number "I don't Dance", but are getting along by the end.
Shipping tends to happen when those who had watch the films as a child re-watch them again and noticed chemistry between the two during "I don't Dance".
Tumblr user batmanisagatewaydrug wrote an entire plot summery for a possible High School Musical 4, that would take place during Chad and Ryan's wedding. The post currently has almost 150,000 notes.