"They are eating despite not being hungry."
Translation:Jedí, přestože hlad nemají.
Yes, "přestože", "ač", "ačkoli" and "i když" are interchangeable in this type of sentence. One sentence is positive and the second one negates it. "Přestože" and "i když" are more common, "ač" and its' longer form "ačkoli" are rarer and rather used in books.
"Jedí, přestože/i když/ač/ačkoli hlad nemají."
"Šel jsem spát, přestože/i když/ač/ačkoli jsem nebyl unavený."
Perhaps this will help: https://dictionary.cambridge.org/grammar/british-grammar/in-spite-of-and-despite
How should it help in particular? You are claiming it is wrong so you have to explain what is wrong.
Despite is usually used before a noun: Despite the weather, despite the difficulties of the Czech language, etc. "Not being" is not a noun. People do talk this way, but to an English speaker it sounds awkward. It is better to say: They are eating, despite the fact that they are not hungry.