Short answer: not yet
Long answer with some spoilers:
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If I remember right (it's been a minute since I read the novel) there's pressure on Chi-young to have kids to carry on the guardian bloodline or whatever and he's trying to keep that away from Heeseong so that he doesn't feel pressured into starting a family. Also something something stress of the pregnancy on his body. They do end up deciding to have a family but he's not pregnant right now.
Wait wait.. so our puppy can get prego ??? Whaaaaat
Short answer: Yes but no
Long answer with spoilers:
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Right now Heeseong can't get pregnant there's a procedure he has to go through to become able to get pregnant. I think it's some medicine or surgery but I can't remember which. I do know that they tested Chiyoung and Heeseong to determine who would carry the baby and it was decided that Heeseong was the most compatible with the procedure lol Chiyoung was upset about it because he wanted to take on the pregnancy instead of having Heeseong do it.
Ah understandable. They just suck at communicating
He's pregnant isnt he