Answer:
In a manner of speaking, yes, you can separate Sodium Chloride into Sodium and Chlorine. The dangers are that pure Sodium is extremely reactive, so much so that it may explode; and pure Chlorine gas is deadly to breathe.
The easiest way to separate the two is by electrolysis. If you fill a container with regular water, then run an electrical current through the water, you will separate the water into Hydrogen and Oxygen.
Use a 12 volt battery, attach wires to each terminal on the battery, and put the bare ends of each wire into the water. Do not touch the wires together, but leave some distance between them in the water. Hydrogen will start to bubble off the negative wire; and Oxygen will bubble off the positive wire.
If you use seawater instead of regular water, and do the same thing, then Hydrogen will still bubble off the negative wire; but now Chlorine will bubble off the positive wire. Do not breathe the Chlorine -- it is amazingly dangerous! In fact if you do this experiment, do it outdoors where you have very very good ventilation!
However, this process will not produce Sodium. It is too very reactive, and will immediately combine with the water to make Sodium Hydroxide. Sodium Hydroxide then dissolves into the water. This occurs so fast, you will not be able to observe it happening.
But at least, you will partially see Sodium Chloride "reversed".
For more information about electrolysis, see the Wikipedia article http://en.wikipedia.org/wiki/Electrolysis_of_water