Does it interfere with the mom's pregnancy? e.g. delayed birth
Yes, you can, with absolutely no effect on the pregnancy. She can even be put back to work, however, she will not fight or put out fires, but will instead flee back to the living quarters during the incident.
Pregnant women work, and can be used in any room. Once they're pregnant just put the parents back to work, it's fine.
The only real difference is that they stop responding to incidents, and instead run and hide. So I'd advise you de-equip any weapons from them, which can then be handed to non-pregnant dwellers.