While her child would be a U.S. citizen if it was born here, the child cannot file for her until it turns 21. That said, she should follow through with her I-751 that appears to be pending. If she wins that case, then she gets LPR status without conditions and then can naturalize in a few years.
A child can only help a parent receive permanent resident status once the child turns 21. Further, your friend should make sure not to jeopardize her future ability to receive immigration benefits by failing to proceed or by provide accurate information to the USCIS. Remember that even if a person satisfies requirements for green card eligibility they also have to show the USCIS that nothing in their past makes them inadmissible. She should discuss this with immigration counsel.
Legal disclaimer: The above statement is only intended to be general in nature and in no is to be taken as specific advice. A complete consideration of all facts is not possible in this setting and is necessary in order to provide any legal advice. This communication does not create any attorney-client relationship.
To answer your question directly: No, having the child in the U.S. will give no immediate benefit to the mother when applying to remove her conditions, and in fact being pregnant by someone other than her husband will raise questions as to whether the relationship was entered into in good faith. I would definitely have her contact a local attorney for an in office consultation to determine the strength of her case and what she will need to do to prevail on her application to remove the conditions of her residency.
BRImmigrationLaw.com: This is not legal advice as many facts are still unknown, and an attorney-client relationship has not been created.
A U.S. citizen child may only petition for their parents after having reached the age of 21-years-old...
This response in no way establishes attorney/client privilege or relationship.