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(I'm a fan of Samurai Jack and I like how Aku's character is written)
Aku would fit the yandere role pretty well, but not in a classic yandere way.
I mean in a way that he's possessive, but he wouldn't really know how to spoil by human means.
He would put the head of your(and his) enemies next to you while you're asleep and give you a big animal to have for a meal. It can range from a boar to a giant edible alien. If you were a warrior and can already do all of that on your own, he would still do that, but he would find you more attractive.
He doesn't stalk you like a yandere usually would either. He would most likely watch you through his "magic tv". As for protection, he already has a henchman or two taking care of that.
As for your "first meeting" with Aku, he would most likely just grab you and bring you back to his tower without second thought. It's funny to imagine him grabbing you in a giant bird form like in the beginning of Wind Waker-
Of course, that doesn't mean Aku's constant spying stops there. He would keep you in a cage or by his side and watch you like you were the most entertaining thing he's ever owned.
You would probably think that Aku sees you as a pet or a plaything to look at. But Aku sees you as a "lover" that needs to be "protected".
And by "protected", I mean keeping you in his room, under lock and key, in his tower, where no one has the slightest clue that you're even in there.
You can hope that Samurai Jack eventually finds you one day, but I doubt he would make it to the tower for a looong time.
So, you might as well get comfy and let Aku spoil you, ok?