No. When the charged object is connected to the capacitor(plate), the charge of the object will reduce as much as the charge increases in the capacitor (if the capacitor was uncharged before). In other words the capacitor(plate) will get the same charge as the object. (Both have either + or - charge). Since the other "side" of the capacitor is connected to the ground, an equal, yet opposite charge will "emerge" from the ground to the other plate. There is now a potential difference between the plates due to the charge differences of the plates, and thus energy is stored. Electrons cannot travel from one plate to the other because of the insulating material between them.
Charge never just "disappears" (in a local system).