You need to reduce the pressure to eliminate the water, so your suggested approach is unlikely to work. A freeze dryer is really what you need, though a very powerful vacuum pump may do the job. You would need to ensure that the sample stays frozen, which is tricky without the right equipment.
What are you trying to achieve here? Is it to stabilize enzymes? Or a desire simply to concentrate the sample? You could for example remove much of the water by ammonium sulfate precipitation Or by using spin concentrators. Dialysis against 50% glycerol will remove a lot of the water and leave a sample that can be stored at -20 in unfrozen state. There are other approaches to removing ~90% of the water, but to remove all of it and get a dry sample with biomolecules well preserved, then it has to be freeze drying.
No, sodium hydroxide is not suitable for freeze-drying. It is not an absorbent and would not be effective at removing moisture from the material. In order to freeze dry something, a vacuum chamber and a source of cold temperature are needed.
No, sodium hydroxide does not undergo sublimation and sublimation is the key factor in freeze drying. To freeze dry, you need a combination of refrigeration and vacuuming. The vacuuming creates sublimation for drying to occur. That is, the moisture in your product will freeze to solid and sublimed from solid state to gaseous state and then the gaseous will be evacuated out of the chamber.