No, nearly all the characters do not find out, BUT an injured, nearly dying, and drug-induced Baltar confesses to Laura Roslin while they were visiting the basestar to ask the hybrid questions about the Opera House in the season four episode, The Hub.
On the basestar, Roslin unsuccessfully attempts to communicate with
the Hybrid, only gleaming the message to "protect the child." During
the Battle of the Resurrection Hub, Roslin attempts to administer
first aid to a severely injured Baltar, injecting him with morpha. As
a result of the drugs, Baltar admits to Roslin that he unintentionally
gave the Cylons the access codes to the Colonial Defense Mainframe,
resulting in the attack on the Colonies. Roslin immediately stops
administering aid and sits idly by while Baltar bleeds. However,
another vision of Elosha convinces her that she cannot lose her
humanity. Realizing this, Roslin helps stabilize Baltar and never
pursues his role in the attack further. When Adama finds the missing
basestar and reunites with Roslin, she tells him that she loves him
He never specifically tells her it was Caprica Six, but he does tell how he unintentionally gave the Cylons the access codes. Roslin almost lets Baltar bleed out and die as a result, until she has a vision with Elosha who reminds her the importance of her own humanity. Roslin never reveals this truth to anyone.