Seawater is drinkable and will, in general, not cause food poisoning. However, this is not the purpose of the question. Although it is possible to drink seawater, it will only make you more thirsty.

Our body contains salts. Amongst other functions, this salt is necessary to regulate the amount of water in our cells. It regulates the pressure in cells and facilitates several processes in cells. The right amount of salt (or other dissolved materials, which will have the same effect) is called isotonic. Not enough salt is called hypotonic, and too much hypertonic.

The body will react to a hypotonic fluid by getting rid of water. It makes you go to the toilet. A hypertonic fluid makes the body require water to dilute the fluid. This results in a sensation of thirst.

Seawater contains too much salt. When you drink it, too much salt is absorbed, resulting in a high salt level in the blood. The body responds by taking water out of the cells. This increases the sensation of thirst. In short, seawater makes you thirsty.