I think it does count as a season of competition and starts the 5 year clock, even if the JC student was enrolled part-time.
See 14.02.7 for the definition of Intercollegiate Competition.
14.2.2.1 says the 5 year clock starts if a part-time student engages in Intercollegiate Competition.
14.2.3.1 says a season of competition is used, with the exception that a JC player may participate in up to 2 scrimmages per year, provided the scrimmages precede the regular schedule of games, no score is kept, and no admission is charged.