I think it is supposed to mean that the three sons coming back (even though they are dead and buried) is a miracle, just like a roasted rooster crowing is a miracle, both attributed to Christ.

Actually, i think this verse is probably an interloper from a different ballad. In "King Pharim" (Pharoah), the King says that if there is truly a child born of the Holy Ghost, "this roasted cock that's in the dish shall crow full fences three. The cock soon feathered and thrustened well/ By the work of God's own hand/ Three times the roasted cock did crow/ In the dish where he did stand."