No - that won't work.. Unless something has changed very recently, "Print member card" is only available for members w/o status.

To the OP: you could take a screen shot of the card that is visible via passbook. But the best option would be to print your membership page which displays your current status, flight activity, etc. and then - if they are insisting on an expiration date - print off the rules/reg page that explains status ends of Feb. 29/March 1 2016 (I can never remember which one it is)