Her husband, Richard Dart (pictured) , is one of three men accused of travelling to Asia for terrorism training.
His barrister, Frida Hussain, told the preliminary court hearing that Mrs Hadi was “to be added” to the prosecution and a date set for a possible trial next year would be affected by the birth of the child.
“She is pregnant and her due date is February 27,” she said, adding that she also suffers a life-threatening condition linked to her pregnancy.
“She will not be in a position to focus on her preparation (for court),” she added.
Dart, of Broadway, Ealing, west London, who appeared in a BBC Three documentary after converting to Islam, is charged with preparing for acts of terrorism between July 2010 and July 2012, alongside Imran Mahmood and Jahangir Alom.
As well as the terrorism training allegation, they are accused of travelling abroad to commit acts of terrorism and advising and counselling the commission of terrorism acts by providing information about travel to Pakistan, terrorism training and operational security while there.
Dart, 29, Mahmood, 21, from Dabbs Hill Lane, Northolt, west London, and Alom, 26, of Abbey Road, Stratford, east London, were arrested between July 5 and 7.
Dart, whose step-brother Robb Leech was in the public gallery, sat in the centre of the three defendants in a green T-shirt and with a black beard.
He and the other two men spoke only to confirm their identities.
They appeared via video-link from Woodhill prison at the Old Bailey alongside a woman, Ruksana Begum, 22, of Provost Estate, Islington, north London, who is charged with possession of a digital memory card containing a document likely to be of use to a terrorist.
Wearing full-length Islamic dress, including a veil that showed only her eyes, she appeared via video-link from Holloway prison.
Alom lives in Stratford, where the Olympics is being held, but Scotland Yard has said none of the alleged offences was linked to the Games.
They were remanded in custody ahead of a hearing in November.