If we make a little step into the real world, calculations should take into account transmission line effects of wires and capacitor.
Thus model could be voltage source, transmission line (charged or uncharged) and an ideal capacitor. Voltage pulse starts, encounters transmission line impedance, reaches capacitor and start bouncing back and forth depending on impedance mismatch.
By the way, capacitor charge curve is only approximated by exponential curve, in reality it is made of little bumps/steps (and steps can be quite big).
Capacitor charging efficiency would be essentially the same, but limit case of [charge time->0] would have different interpretation