No. The FBI got all they were going to get. None of it can be used against him in court, and the Miranda Reading had to be done sooner or later, else he could escape prosecution.
Besides, had someone NOT read him his Miranda Rights (him technically being a US citizen and all), it would set a DANGEROUS PRECEDENT for the rest of us actual AMERICANS.
He could not escape prosecution because he was not Mirandized. There is plenty of other evidence, not the result of this interrogation, that could be used to convict him. Miranda is not a get out of jail free card.