Yes, normally, but in the gamified fanfiction that is her Origin, she is Tav and hence desirable and desired by any and all. Including the bad boy beau bloodsucker, who squeezes her name into basically every line during their modified tête-à-tête in the woods, so that it really does sounds like exceptionally clunky fanfiction, dreamed up by the horny-teen-soldier who desperately needs romance in her life.
Whenever I feel a little disgruntled that they didn't even bother to change the approval for blood drinking during sex for Gale, the way that scene was handled with Karlach reminds me that there are worse things than neglect.
Edit: As someone who does like playing Origin characters I do appreciate it when situations are modified to fit the Origin. Usually those are either things that are meaningful to the character or small modifications made to better accommodate the character. The reason why I - and I think a lot of other people - like to make fun of the modification of especially Astarion's romance to fit Karlach is, because it's so disproportionally big, tailored to one specific romance and very fanficy in nature.