edit addedYou could, but many AE speakers won't understand it. It's what an AE dictionary would label "chiefly British" or such.
very tired [Princeton WordNet- no mention of UK or BE usage]
Amer. HeritageChiefly British
Very tired; exhausted.
Random House UnabridgedBritish Slang. exhausted; very tired:
Quite a few AE speakers would understand it with no difficulty. Even those unfamiliar with the term might be able to figure out the intention from context, expression, body language, etc.