Suppose one plate of the capacitor is grounded which means there is charge present at only one plate. We know that the potential across the capacitor will be 0, i.e., V=0. And capacitance of the Capacitor will be C=Q/V C=Q/0 implying C=∞ So it means that the capacitance of a grounded capacitor is Infinite.
In open circuit, no charge flows. If we connect both the capacitor plates it makes closed circuit, charge flows in the circuit, as a result charges on the plates neutralizes to zero. If only +ve plate of the capacitor is only connected to ground there is no closed circuit. no charges flows from the ground.
You're charging a capacitor made up of the Earth as one plate, and the ball as the other. The capacitance of this capacitor is very small, because the "plates" are so far apart, so to move any noticeable charge, you need to use thousands of volts. For flow of charge, the circuit should be closed. In open circuit, no charge flows.
When a capacitor is being charged, negative charge is removed from one side of the capacitor and placed onto the other, leaving one side with a negative charge (-q) and the other side with a positive charge (+q). The net charge of the capacitor as a whole remains equal to zero.
It is possible to add charge to one plate of a capacitor, but you won't be able to add very much. It's like charging a metal ball. In this case, you're connecting a voltage source between the Earth and the ball, and moving charge from the Earth to the ball. You're charging a capacitor made up of the Earth as one plate, and the ball as the other.
From this we may see that earth (ground+atmosphere) is a capacitor itself. It was experimentally checked that the ground has negative charge and so it is the source of electrons. So in your question you plug one capacitor to the half of the other one with huge charge. The answer is - no it will NOT discharge COMPLETELY.