Does gravity affect the efficiency of heat pipes?

Question

Physics

We take the classic modern cooling system for the processor - heat pipes, radiator, propeller. We install this system vertically. (Processor from below, tubes from above) Turn on the fan at maximum speed. We begin to remove heat from the processor.
We carry out the same experiment, turning the system upside down (tubes from below, processor from above).
Will there be a difference in CPU temperature in the first and second cases? How big will it be if gravity plays a role?

Answer 1

There will be no difference.
Gravity does not affect heat.

Answer 2

Heat pipe, heat pipe (English heat pipe) - an element of the cooling system, the principle of operation of which is based on the fact that there is a low-boiling liquid in closed tubes made of heat-conducting metal (for example, copper). Heat transfer occurs due to the fact that the liquid evaporates at the hot end of the tube, absorbing the heat of evaporation, and condenses at the cold end, from where it moves back to the hot end.

If the heat pipe works exactly like this, then the efficiency may decrease - the evaporated liquid will stupidly fall down less efficiently and cool less efficiently.
On the other hand, the capillary effect more likely works there, which is written about on the same wiki.