If you can get a rep to notate your account saying you will get the points after getting the additional cards you should be good to go. Once you get that notation saying you're eligible you're fine.
I spoke to a rep today, and while looking at my account she said, "did you call yesterday about this?" I said I did but got disconnected. She said that the account was already notated with 5721, but she'd add it again. Then she transferred me to Cust Serv.
Even though my account was notated, the CSR said I needed to follow the steps in the email or snail mail offer. She said that in addition to the offer code, there was a unique code needed to "keep it fair" since the offer was posted on the Internet.
Sigh (again). I'll keep trying.