Do you know what the difference is between a gnarly blue belt and a shitty new purple belt? Nothing. Someone at your gym has to be the worst purple belt. Why can't it be you?
You already know how to fix it once you get promoted. If you feel like you aren't ready, go train until you are. If you feel that your promotion was on time, go train and show how right your coach was to promote you. If you feel that your promotion is long overdue, go train, and show that you're well on your way to your next belt.
Embrace the grind, and enjoy your purple belt when you get it. Just know that once it starts feeling really comfortable around your waist, you'll be on deck for your brown belt.