Spoiler
He does. Zigryl tries to take him with him to the capital because he wants to continue fucking him until he loses interest, then send him back home with some money afterwards.
Kay does not like these plans and tells him as much, which pisses Zigryl off enough to cook him a meal with the flower of alosha in it. Kay is dumb enough to actually eat it, they fuck, he gets preggo. His attempt to either abort the child and/or flee the capital are about as successful as one would expect, which is not very much.
Turns out, Kay is a noble, whose family Zigryl had previously killed (but he didn't find Kay at the time), but that means Zigryl (who has killed his brother and took the throne) can legally make Kay his empress as well as, that he'll be killed by the people in the capital if he chooses to NOT become his empress, because the don't like the old noble families there very much lol (probably why Zigryl killed them all previously).
Kay doesn't want to die, so he agrees. He doesn't love Zigryl and since the child takes VERY MUCH after Zigryl in both looks and behavior (both are obsessed with Kay to the max), he doesn't like the child too much either.
He basically just accepts his fate thinking, it could always be so much worse (or e could be dead and he doesn't want to be).
Does he get pregnant? I feel like that’s where this is going.