I would doubt
if you can get approved if you apply through the mailed offer now. They can deny you with the reason of you having the product, and/or have a recent application or whatever. But it might turn out they approve you, so calling and asking them should get you the answer.
If you want anyway to get the bonus from the mail, look at some discussions in FlyerTalk (1
). It looks like many people used to successfully match offers, but now it has been pretty difficult. Can't say it's impossible now if you find the right approach, but it can really be a hard one.