You'd get "dead blow thrusts", while normal swinging (due to centrifugal force) almost always pushes the mercury to the tip of the sword. You'd essentially be swinging around a sword with a heavier tip and mostly hollow blade, except while thrusting, where you get the "dead blow" effect.
Until you realize what a thrust really is. Having the hollow blade + mercury in the middle is useless, because a dead blow thrust is useless. A thrust is a singular motion - by the time the dead blow action kicks in, you've already fully penetrated your target to your swords maximum potential, especially since the little bit of dead blow weight from the mercury pales in comparison to the amount of force you're pushing into the sword when you thrust.
This: ...causes the blade's weight to "shift backward when raised and rush forward when swung" does not happen.
So really what you have is a poorly designed, weakened sword.
In this case, your assumption that this is supposed to give forward strikes more force is flawed.
Such a design, however, does take away from the sword's effectiveness (if you're looking at the effectiveness from a "how long will this thing last/how likely will it break" standpoint.
Actual effectiveness in combat will depend on the training of the user.
Clarification: A "Dead blow" is when a part of the force of a strike hits the target after the weapon has landed. For example, a "dead blow" hammer is often hollow on the inside and filled with sand (or something like that) - when you swing the hammer, the hammer first connects with the item you're trying to hit, but the force from the sand doesn't connect until a split second later; when the sand travels from the back of the hammer to the front due to the hammer stopping. The point of a dead blow is often to distribute the energy of a strike over a longer period of time, and to minimize rebounds.