Sink overflow drain not cast all the way through
Probably not, unless it's just lightly plugged with a thin flash (eggshell thickness or so) you can break through without breaking the overflow channel (either out to the underside or in to the sink bowl.) If it's a plug of thickness similar to the channel walls, I doubt you'll get through it without going wrong in one of those directions.

This should have been inspected and found at the time of original installation when it would more easily have been resolved by return to the supplier for a correct one. If you have a really top-notch supplier that might still be possible.