I would be surprised if your explanation would hold any sway; but they might decide just to drop it so as not to spend any more time on it. I can not imagine an urban parking fine being excused because you tell them you were "in a hurry" and didn't want to take the time to put money in the meter (unless it was an emergency situation).
I don't enjoy taking the time to fetch those little envelopes, put $3 them, and slide them in the slots either; but I do. What is the point if other people get away with not paying just because they don't feel like taking the time? Hikers get enough guff from hunters, fishers, snowmobilers, and ATV users for supposedly not paying our fair share into the system. Why give them more ammunition by avoiding a little parking fee?