Hola Emelie! Sí, significa lo que crees. Es una frase un poco de mal gusto,pero en ese estilo musical suelen decir cosas de ese tipo. Saludoss

Just like these guys have already told you it means this: "I swear I'd do whatever, so you belong to me with your body and your heart" So, he wants "to possess" her physically and emotionally. That's why he used the metaphor speech, by saying this "por ser tu dueño - to be your owner" referring on this.. "to be the owner of her body, heart and soul" I hope this helps. If there is anything else I can help, please, don't hesitate to ask me :) Good night.

I wouldn't say affectionate as it sound kind of obssesive to me, but yeah, I guess that's the point. "to be her owner" poetically, meaning possesing her, with both romantic and sexual connotations involved.

I´m agree with the previous coments. Litterally means "to be your owner" trying to be romantic... It´s a sexist song :S