If I hear you say アルコールはダメなんだ without any context, I will understand it as "I can't drink alcohol".

That said, ダメ is certainly an absurdly polysemous word with general negative connotation "not good; don't do; don't work". Alone it won't even tell what is not good to what, so the context eventually matters.

Instead of using your example, I will present a Hatsune Miku song called 胸いっぱいのダメを (YouTube), from which you can have every imaginable shades of the word usage...

空気が読めないからダメ An insensitive guy (like you) is useless.
心を見透かしてはダメ Don't read others' mind.
ダメダメいうのもダメだ Stop saying "no, no".
その着地点もダメだ That solution(?) is no good either.
無責任な本音はダメ A blatant truth is not allowed.
中学生のダメを ... faults of middle schoolers [accusative]
不老不死ならもっとダメ Immortality is even worse.
焼き肉がほんとうまくてダメ The grilled meat tastes so wickedly good.

If I hear you say アルコールはダメなんだ without any context, I will understand it as "I can't drink alcohol".

That said, ダメ is certainly an absurdly polysemous word with general negative connotation "not good; don't do; don't work". Alone it won't even tell what is not good to what, so the context eventually matters.

Instead of using your example, I will present a Hatsune Miku song called 胸いっぱいのダメを (YouTube), from which you can have every imaginable shades of the word's usage...

空気が読めないからダメ An insensitive guy (like you) is useless.
心を見透かしてはダメ Don't read others' mind.
ダメダメいうのもダメだ Stop saying "no, no".
その着地点もダメだ That solution(?) is no good either.
無責任な本音はダメ A blatant truth is not allowed.
中学生のダメを ... faults of middle schoolers [accusative]
不老不死ならもっとダメ Immortality is even worse.
焼き肉がほんとうまくてダメ The grilled meat tastes so wickedly good.