A hole in a circuit board that carries an electrical current is called a via. Vias consist of a donut of metal on the top side of the board, a cylinder of metal coating the sides of the hole internally, and another donut on the bottom side. Since there isn't a trace connected to the top side, the signal the via carries comes from the bottom of the board, which is luckily intact.
So as long as the pin that goes through the hole extends far enough to be soldered on the bottom side of the via, you'll be fine; the electrical circuit will be complete and it should work the way it's supposed to.
All in all, I think you're okay even without that top pad.
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