Quick question- refunds on annual fees after spending once?

If you are late (but not very late- within 30 days) of cancelling a card with an AF and asking for a refund, but you have spent it at least once after being charged the AF, can you still be refunded the full AF, or are they more likely to prorate it? Or is prorating entirely dependent calculated based on number of days past the annual fee you are over, and nothing to do with the activity?

Also, should you pay your card (for that purchase) even though the statement obviously isn't due before you call to cancel?

(CSP by the way. Not really interested in downgrading because I already have 4 Chase $0 AF cards and I don't really want a 5th.)