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I used to take N.A.C. as a health supplement it's an amino acid, and did not ever smell like sulfur, a bit like vitamins at worst. I took it on the basis it can help create glutathione, and reduce inflammation. It's actually one of the pills I will put in my mouth before finding water to drink since it tastes like a gelcap and then nothing if it dissolves. You can buy it at a health food store no dr. needed. No this doesn't mean you should od on tylenol or ever take it if you can avoid it.
"New treatment" = mental health
The headline made me think it was something actually new >

Could you take acetylcysteine to mitigate possible damage from the combo? >

You are not likely to be prescribed acetylcysteine by your doctor beforehand if you intend to take a pill before getting hammered and then take Tylenol for the headache, like 1 hour after stopping to drink. I should also state that the chemical composition of N-acetylcysteine contains a sulfur group, meaning the medication will smell. It is known the tablet form is horrible to take.
Just keep drinking water to stay hydrated. I drank a bunch of Pedialyte to stave off a headache with better success than Gatorade.