Possibly. He's very resourceful. But he's also human (twisted and disfigured soul, but yes, human) and therefore he makes mistakes. Trewlaney didn't even know she made the prophecy, only Dumbledore and Snape.
Even though Voldemort had spies at the MoM, Dumbledore never worked there. He was only offered the position, which he refused.
If you took Snape out of the situation altogether, it would all come down to whether or not Dumbledore kept quiet about what he knew.