No. There is no way they can be forced to cover her. If she is not a dependent under the terms of the insurance contract, then she is not entitled to insurance coverage under your policy. Nothing whatsoever in the law says that they HAVE to even cover your spouse, let alone your pregnant girlfriend. For that matter, they don't HAVE to provide insurance coverage for YOU.
You have no recourse except getting married, after which IF YOU PROPERLY ADD HER TO THE POLICY they will pay for any treatments AFTER the date of the marriage. If you don't want to do that, you have no recourse at all
They will not be responsible for your girlfriend's care when she gives birth, either, btw. Under Illinois law, they must provide care for a newborn - my source does not say how long, but traditionally most states that have such a requirement, require 30 days. That care will be ONLY for the BABY, NOT for the mother. Her bills are entirely her own - or your - affair; your insurance has NO responsibility for them. You will have to actively add the baby to your insurance plan for them to have any responsibility for him/her after the 30 days, as well.
I just caught that the mother lives in Missouri. Missouri does NOT require newborn care. Therefore, you will have 30 days to actively add the baby to your plan, or the insurance will have no responsibility for the baby, either. Forget everything I said about Illinois law; it doesn't count.