No, a stunned toon hasn’t taken a turn yet so when they become unstunned, their abilities are still increased.
You should be able to notice that anytime you have done this. They will open with a basic. Should someone not I feel the problem is we all play on 4x speed so can miss seeing an enemy not get it’s cooldowns increased.
Try a battle on 1x speed and really focus on the numbers and words on the screen. Arena is always the same for me and I pretty much only look at TM bars...the rest is just background, like driving, and I react accordingly.