Yes elves could be poisoned. Aredhel the sister of Turgon was killed by poison in the Silmarillion by Eol.
Quote:
But in the evening Aredhel sickened, though the wound had seemed little, and she fell into the darkness, and in the night she died; for the point of the javelin was poisoned, though none knew it until too late.
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His sword was long his lance was keen
His shining helm afar was seen
The countless stars of heavens field
Were mirrored in his silver shield
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