[quote name='simmias']Yes.
Yes. However, I don't think you are grasping exactly how it affects your score. The major factor in your credit score (besides timely payments, no judgments, bankruptcies, etc.) is utilization - debt/available credit. Opening a new card will not make that ratio worse... in fact, it will help your score because now you have more available credit than you did before. You will take a temporary hit in your length of credit accounts and your number of recent inquiries, but who cares unless you're applying for a mortgage or loan in the next few months? In the long run it's always beneficial to your score to have more credit than less as long as you are responsible.
More potential debt helps your score, actually. Not having the willpower to keep from maxing it can pitfall it in a hurry, though.
Congratulations on tackling your debt! When you're done, visit a place like the finance forum on fatwallet.com. You'll learn more than you ever wanted to know about your credit score... more than Dave Ramsey can tell you

(I'm guessing Ramsey? You did use the term "debt snowball")
And you said it yourself - they send you a warning. Just read your mail, give them a quick call, and you're done. Even if you don't read your mail, read your statements. If you see that they decided to start charging an annual fee, call and cancel the card - they have to remove the fee under the new legislation as long as you are reasonably timely.
I didn't think I gave you any lip, I just wondered why anyone *wouldn't* have this card in his or her possession. And no, I wouldn't bother with the rewards program without the card, although plenty of people do. Read through this thread - your question has been asked and answered several times before.[/QUOTE]
There is one thing that's not 100% true. If you have too much credit, your score goes down. I was at a lecture with a financial adviser, and he's seen a case where a guy had 200k or so in credit card limits, and that brought his credit rating down. They're afraid that someone could charge it all up and disappear if it gets too high. But of course, who has $200k credit lol.