Unless they have a busted ventromedial nucleus of the hypothalamus, yes.

If that's shot, they'll eat until they burst, but that's very unlikely - though the cause might be glutamate toxicity.

It might happen with people with poor gut barrier function if they consume a lot of wheat; wheat-germ agglutinin (WGA) binds leptin receptors, blocking them. Leptin inhibits hunger. Similarly, WGA also binds insulin receptors, so it's a bit of a double whammy; it takes the brakes off hunger and increases blood glucose, causing it to be more likely to be stored as fat. Regardless, hunger increases.

You seem to be quibbling over the definition of satiety. Satiety means "feels full/done with food". By definition, if someone experience satiety, their hunger is sated, and stops.