Because of the affordable care act, no (thankfully, as pregnancy was a pre-existing condition) but your insurance may not cover a doctor or hospital which could (even accidentally) add up to thousands of dollars. Ask who people are when they walk into your room, and whether their treatment is covered depending on your insurance.
Not sure why this got downvoted - pre-existing conditions are covered by law but that doesn’t mean the procedure at that hospital is covered at the same level as an in-network shop.
I’ve been charged out of network at an in-network hospital because the physician didn’t identify themselves or their network. If they’re not your primary doc it might be worth asking for someone who is covered to save you hundreds or thousands of dollars.