Salt is an oral and gastric irritant. In fact, the hypertonic salt water is used as an emetic that makes you vomit. So you will puke it out.
Excessive salt intake results in a physiological condition called hypernatremia, surplus of Sodium ions. This electrolyte disturbance is managed in the kidneys and it attempts to correct it by flushing it out via urine.
Extreme thirst, nausea, weakness, loss of appetite, abdominal cramps, headache, rapid pulse, increased blood pressure, muscle twitching, altered mental state are some of the starting symptoms of this condition. At a higher range arrhythmia, cerebral hemorrhage or peripheral edema, seizures and coma can happen. But a lot of this depends upon the age, gender and other health conditions of the person.
People who die from acute salt poisoning usually have other comorbidities like an inadequate or impaired water-ion regulation (thirst mechanism). Generally, fatality is observed more in children under the age of 6.
Basically, it is a very unpredictable and torturous way to die. Body has inherent defense mechanisms to ward off that possibility.
TL;DR: Common salt, NaCl, is not suicide friendly. Do not attempt to use it to kill yourself. You'd suffer unnecessarily.