Copper is actually ~25-250X leas efficient at transferring heat than a heat pipe and convection is hundreds of times more efficient than radiation at transferring heat and the fins on a heat sink would have hundreds of times less surface area for dissipating heat all that is to say this might work but it would be orders of magnitude less efficient than a standard heat sink.

Water moving is much better at removing heat than heat pipes could ever imagine. It depends on how fast the mass of water is moving.

I’m pretty sure the way heat pipes move heat is with water funny enough