Shove it in, and post up their response when you get it.
I think Bristol realise they have boobed with their PCNs, but as most people just cough-up the penalty, they carry on with them. I suspect they will not reject your reps outright, but "make you an offer you can't refuse". So far nobody has managed to get to the Traffic Penalty Tribunal, they just let it die on the vine until the 56 days are up when the reps are automatically accepted by law.
There is something going on inside their CAZ management, but at the moment, the situation is not clear. The Birmingham CAZ PCNs just have the PCN penalty on them, and their CAZ Order specifically states that payment of the PCN discharges any liability for the CAZ charge. They were clearly better advised. Other CAZs are the same as Bristol, as is the DART system under the same legislation and regulations.