OP, this happened to me last October when I PC'd to the AA card:
"So the same night I PC'd the card, I noticed my online account showed the new AA card with a new account number (last 4 digits). I decided to call to add an AU (you can't do it online while an account is pending).
Long story short, the CSR said "I'll go ahead and overnight the AU's card and waive the $6 fee". I told her I thought my account wouldn't convert until 51 days later and she said "Well I see an American Airlines WMC account is already created and the old one will deactivate as soon as you activate your card, did you receive you card yet?". I told her no and she said she'd overnight my card as well.
Got both my cards this morning and both working perfectly. The old ThankYou card is not even on the site anymore!
So for future PCers, it really doesn't take 51 days like they say! Literally 2 days to receive the new card! Of course and as always, YMMV."
My conversion actually took exactly 51 days like they said, the conversion letter came in the mail 51 days later and they charged the AF. However, since the account online was already switched the day after I PC'd, i just called them to expedite the card(s) and so I used the card and earned miles 2-3 days after I PC'd. But the "official conversion" with the AF charged was 51 days after PC. FYI for those who can do the same.