I too am in to all sorta of overclocking and such.
The problem I have with liquid cooling systems is that they are contact based systems, and only cool major components (e.g. CPU, GPU or mem).
The problem is, as you overclock a system you are putting more stress on everything, not just the major components. When you start to get into the super-overclocking as you are talking about, I have no doubt that it is fairly easy to remove all the heat generated by a CPU overclocked 1000%. However, you are doing nothing about cooling the rest of the system in such cases; which I suspect is a large problem.
Back to your original idea. It could be done actually, but you would want to install some sort of pressure relief system; as such when the pressure gets to high due to gaseous nitrogen, it lets the gaseous nitrogen out relieving the pressure.
As to how often this will be required and how much liquid nitrogen in a day; A lot of variables factor that. One major factor is the target range you are trying to hit, and ask you asked, how cold is to cold. I am not personally sure, but it is irrelevant as well before you get to the point where it damages the system, you get to a point where the cold actually has the same effect as the heat and causes errors. Read the detail specs of the CPU at the website, it should listed recommended operating conditions. Yes, if you go below the recommended operating temperature you can actually causes the system to run slower.