She's got at least 3 or 4 months to do that before it becomes unavoidable. I've known women who did that. I know one guy who had a woman call him up 4 years later and inform him he had a daughter, and then ask for child support. He had no idea.
For the record, once the paternity test came through, he paid it without fuss, and actually got involved in her life.
He can't tell the court if he doesn't know.