As StuMc says, it hasn't been a big deal not to have your Elite Card as long as you're in the system -- and *Alliance partners seem to have that info also. I can't speak for international airports, but other than the potential upgrade problem, this may be no more than a temporary inconvenience. There are more things about AC to worry about (like their heavyhandeness with flight coupons and U/G certificates) than a couple of extra days waiting at the mailbox.
Mind you, if mine hasn't arrived for my LHR flight on the 23rd I'll be really upset
