All of the above doesn't even matter really...there are several reasons this is a bad idea:
The heatpipes are designed to move heat, they are filled with a liquid and also are depressurized compared to normal air to lower the boiling point of the liquid used. The liquid inside warms, evaporates/boils, then re-condenses again in the heatpipe.
Kind of when you boil water in a saucepan with the lid on, pretend the saucepan only has 1cm of water in the bottom, and take most of the air out of the saucepan. It will boil, condensate on the lid, then drop down to boil again. Surrounding the pot, you weld a giant heatsink to help it condensate faster and cool again so it can re-boil and to control pressure.
When you freeze a heatpipe heatsink below the freeze point of the liquid, or cool it down too much, 2 things happen:
1. The pressure becomes lower, making the heatpipe want to implode
2. The liquid inside will not boil...you can't transport the heat from the base to the part where the fins are...
So in essence, it can become a safety hazard (depending on how much you chill it) and it will also not perform as intended, possibly very badly...actual CPU temperatures may be higher than they would be in normal conditions.
I don't know if you guys realize how Vapor-chamber heatsinks work too, like Vapor-X, but essentially they are a flat, square heatpipe.