Bearing in mind that salt is an essential ingredient in food, it is slight incongruous that the famous Pet Poison Helpline, the top search result by Google for the answer to the question, states that salt is potentially poisonous to cats. However, the operative word is ‘potentially’ because salt is ‘an essential mineral for life’ according to Iams, the pet food manufacturer. We know it is a essential food in a number of ways such as for maintaining proper nerve and muscle cell function.

So, this is all about the quantity of salt that a cat ingests. Too much and it is essentially poisonous. The correct amount and it is essential. For humans, and the same applies to cats and other animals, a high intake of salt raises blood pressure. So overweight humans and cats who are predisposed to high blood pressure need to control their salt intake. Reducing salt is one way of managing blood pressure.
Iams state: “The Association of American Feed Control Officials recommends that dry cat foods contain at least 0.2% sodium for maintenance and to support normal growth and development. These are the minimum recommended levels.”
The Pet Poison Helpline does not tell me the quantity at which it becomes a poison. So common sense applies. And I think we can nearly always rely on our cat to apply common sense too. A cat is unlikely to gobble down a ton of salt because it tastes horrible but some cats like to lick salt lamps for example proving that some cats particularly like the taste. And cats like licking sweaty human hands, another sign.

And a cat might get hooked on licking the salt off a human product such as salted nuts (or the salt lamp show above that nearly killed a cat) and they might be given a salty treat by their owner. If this habit persist for too long it might cause a health problem in the cat. That is how I see salt poisoning occurring in domestic cats with respect to foods.
It comes down to the owner’s behaviour in allowing their cat to snack too often on salty human food. I suspect cats vary in their attitude towards salty food. My cat likes prawns for human consumption. They must contain salt to enhance the flavour. So he likes the taste of salt but only to a limited extent. I watch the amount I give him to keep it in check but I am confident that he self-regulates his intake.
The answer to the question is: Yes, in large quantities which a cat is unlikely to ingest under nearly all normal circumstances but it can happen.