While on the surface this might seem to be a good idea, in actuality, this is a very bad idea.
There are two metals (not including alloys) that are liquid at room temperature: Mercury and gallium.
First off, mercury is extremely toxic and should only be handled by experts.
Gallium will corrode aluminum and steel, which is what the coolant runs over/through to sink heat. It will eventually destroy the joints and heat sinks, which will lead to the next problem.
Both mercury and gallium are electrical conductors. If either of the two liquids were to leak onto the electronics, it could cause shorts and even damage the electronics. And again, mercury is extremely toxic. This alone is a reason not to use them.
Mercury and gallium have a high rate of volumetric expansion due to heat. Under high heat, they can expand greatly and the pressure would destroy the cooling lines.
Gallium itself isnt a liquid at room temperature. It has a melting point of 85.58°F (29.76°C), which means of the PC was turned off and it completely cooled, gallium would solidify. This of course could cause problems, since the liquid would not be able to flow.
Editing in some more thoughts:
Mercury is very, very heavy. One liter of mercury weighs a hair under 30 pounds (13.5 kilograms). One liter of gallium weighs 13.02 pounds (6 kilograms). It would take a massive pump to move that liquid around. The weight alone could cause PCBs to flex or break.