OP, I have to apologize and say yes a gaited horse can trot and it won't ruin it. Just as long as you still keep training to gait. It will only take some ground training with posts just as some trainers use to teach them to gait. I happen to know of a lady who participates in many types of events with her gaited horse. A truly gaited horse that has won many awards including the highest award within her breed. During a recent event there was a part where the horse had to trot and her horse did without damaging any of the natural gait bred into her.
I would hope you would still work with your horse to keep its natural gait too, as that would be a loss to you later on down the road if you chose to go back to gaiting full time. I still doubt you would win many firsts, but if you have fun doing it you've won anyway. Ultimately this is your horse and our opinions are just that - opinions.