Not necessarily... Paying a billed item doesn't necessarily validate that item one way or another... You don't give specific info on closing dates, but I'm guessing that if you were to just pick up the phone now and say you had decided to cancel the card, you could get the AF refunded.
So your question is in some sense, "Have I already tipped my hand?" Again, not necessarily. You could call and say, "You know, Friday I was paying bills, paid the BGR, and then it hit me, 'Hey, I just paid the AF,' and I've been ruminating since whether I really want to keep the card another year..." and then just take it from there. If the whole thing ends up being decided by your credibility in the call to the CSR, you're probably back where you need to be.
It may not matter. My sense is that more and more our negotiating skills count for less and less in these things -- it's predestination, you're either among the elect or you aren't, some algorithm at Amex has either put an offer for you on the CSR's screen, or it hasn't. But, sure, why not at least find out, i.e., don't use the fact that you paid a bill on Friday keep you from calling in to try.