Ok, should I add this in the appeal or just await the rejection and submit to the adjudicator?
It's a two stage process. For a PCN served on the scene whoever has the PCN can submit an informal representation challenging it. Get it delivered to the Council within 14 days beginning with the day the PCN was served and the Council will normally re-offer the discount if they reject. Most informal reps are rejected out of hand.
If the PCN remains unchallenged and/or not paid within 28 days then the Council can and likely will serve a Notice to Owner on the Registered Keeper of the vehicle on the day of the alleged contravention. If that happens, even if the response to the informal representation is still outstanding, then the RK must either pay up or submit a formal representation within 28 days.
If the formal reps are rejected then the RK can appeal to the independent adjudicator.