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If the card is attached to your AA account, it doesn’t matter if it’s physically in your possession or not.
When you log into aa.com and go to your account summary, do you see “AAdvantage card member” under your name?
If so, the benefit is to live with or without the card.
If not, having the card may not help you.
If you don’t see “AAdvantage card member,” I’d contact Citi and ensure it’s associated with your AAdvantage number.