itch.io

Yes. If you enable them in court, and go to the court, you can ask them in conversation "when are you due" - they will tell you the amount of days. The closer they get to that date, the more obviously pregnant they will look (belly swollen etc) - and once the day comes, out pops the baby, fully grown already. They will have the same last name as their parent (I think as their mother, but not 100% sure about that), and they will inherit a mix of genes of their parents, as well as one of the randomly selected genders and races. Additionally, the child will always possess the "virgin" perk trait (naturally). 

Here is an example of what a child might look like:
If a fiend male and human female have a child, the child can be, for example, a human female with the "leg type Hooves" and "fiend wings" despite being of human race, but possess "pale" skin that the human mother has (basically, the child is considered a human, but has many characteristics of a fiend.
GAME issue that comes with the offspring and gene inherition
Now, since "vagina" and "penis" are both considered genes, the female child will likely also possess the penis trait, inherited from the male parent. There is no ingame way I found out how to remove the "vagina" or "penis" trait from a character once they possess one. This means a "female", which is not characterized as "futa" in the game, can still impregnate other females with a child, or a male with vagina trait can be impregnated. The only way these traits can be removed is by quitting the game and forcibly adjust them in a "save file". Save files can be found in the game folder under Dungeon Keep Her_data in folder "saves" and can be edited with "notepad" - inside, use Ctrl + F to enable "find feature", type the name of the servant and find the correct one, then use find feature to find the "penis" or "vagina" gene trait, and remove it, save the file and restart the game while loading this file. You can also use this to edit the characters forcibly with perks you might want (for example, I give all the servants and prisoners  I plan to keep the "Barren" perk trait, which makes them unable to have children. It basically acts as a contraception since there is no way in the game to brew a potion that would do the same. If I wish to remove it later on, it is as simple as using a red crystal on them to remove this "detrimental" perk.