No.
You don’t sulk. It’s not about being unhappy. It’s using your unhappiness as an excuse to stonewall and give the silent treatment, to punish someone you claim to love without ever communicating why until they “beg” you to tell them why (or likewise, beg you to stop telling them why for hours on end if they’re stuck somewhere with you, like a car). It’s pathetic and useless, it’s not acting like an adult. Adults communicate.
If you don’t want to stand in line for a ride at Peppa Pig World for three hours with your child, you need to communicate that. If you don’t want joint money being spent, you need to communicate that. And if you don’t agree with your partner, you break up.
What you don’t do is give them the silent treatment, make them walk on eggshells over it, treat them to Narcissism’s Greatest Hits… when you’ve communicated nothing. Look at how many of these specify that the poster paid for the whole vacation and her partner still sulked because sand is sandy, etc. It’s sad, and it’s wrong.
If someone doesn’t “fight fair” with you in your very first fight, if they display any of these behaviors, like the silent treatment or stonewalling or sulking, I’d drop that relationship like it was on fire.
EDIT: That said, I’ve also never said someone was “sulking” in real life simply because it seems like it’s easier to be more specific. Are they giving you the silent treatment? Are they being verbally abusive to you no matter what you say? Are they replying “yes, whatever” and literally sticking out their lower lip to everything? Is he still wildly upset over a situation that ended days ago? What someone calls a “sulk” can vary widely which is why you have these stories. Quite a few of them are emotional abuse.