Karlach would never agree to that, and if we did it anyway, she would hate us for it. Would it be a price worth paying?
Tbh I don't think she would hate Tav for exchanging themselves for her. Hurt, pissed, yeah, sure, never ever would she want them to do something like that, but it's not a hate-worthy sentiment. Heartbreak, maybe. She's definitely the type to be like "DID I FUCKING ASK YOU TO SACRIFICE YOURSELF FOR ME".
If it's like a service contract and not a 'sell soul forever' deal (I don't think Karlach's soul is sold to Zariel, it's never mentioned, she's more of a physical slave mixed with a gun for (forced) 'hire'). Selling your soul might elicit stronger emotions, definitely.
But also if the deal with Raphael is any indication, her reaction would be less hate and more "How do I get your stupid ass out of this" (agree with Orchid there).
Now, is it a worthy price if she does 'hate' us - roleplaying question, I guess. My Tav would take her being alive somewhere else and wanting nothing to do with her over her being dead, no hesitation.
You're not just sacrificing yourself for her. You're selling yourself to Zariel. You're essentially doing to yourself what Gortash did to her. Not only will she be heartbroken that you're now enslaved but she will be doubly hurt by the fact that you've enslaved yourself to the one that enslaved her. Even if it's temporary.
