It can, but it's probably inappropriate to go on lewd adventures while carrying a baby around with you
You can put it in the protagonist's room as an NPC.
Who's gonna take care of it while you're gone? XD
Let other NPC take care of the children.
Will you think about it?
I'll see. The more important question is what sort of changes it brings to the game
You can refer to Love and Corruption
You can do it bit by bit. For example, the character can interact with the child (play, breastfeed)