It is possible, however, unlikely, to kill Cenarius without chaos damage. The game continues the same, however, except that you see green Grom talking to Mannoroth in the end of the mission.

Whether this is merely a game mechanic, or the actual possibility of defeating Cenarius that, in fact, existed, will forever remain unknown because nobody cares. Bear in mind that, while demigod Cenarius was canonically killed by fel orcs, the WoW raiders canonically defeated a number of demigods and gods without succumbing to fel. Perhaps, if you hit it for a while it will die eventually, no fel required?