The Thermal Conductivity of water is only about 0.6, compared to about 200 for aluminum. Even cruddy stainless steel is about 16.
Other common liquids are all worse than water. But even .6 is much better than air (.025) and about the same as common thermal paste/compound.
So, water comes in handy as thermal paste substitute for quick easy experiments. But filling a copper pipe with water does not increase the total thermal conductivity much, unless the water moves due to convection or other flow.
But I do think there are some special situations where water could be useful even if it is not moving. Copper is the best common conductor, but it is both expensive and not readily available in bar forms. Copper pipe and fittings and solid copper wire are very available, both new and salvaged. Nesting 1/2, 3/4, and 1-in copper pipe would increase thermal conductivty - filling such a nested arrangement with water and sealing might be a good practical way to get good group heat flow. Even better, pack a copper pipe with new or salvaged #4 or #8 AWG solid bare copper, available by the foot from Lowes or HD. Filling with water to spread the heat might be much more convenient than trying to figure out how to solder it all together inside the pipe (and much less dangerous).
The makers of power LEDs design for the heat to flow out the backside. The heat does not care which way it flows -- it only cares how easily it flows. It is much more important to do a great job of getting the heat out the back than worry about the tiny amount of heat at the front (if the back is well cooled).