I don't see it working that well. I can easily see him bringing elements of his indy character into his WWE one like we have already seen and as Punk has done . But I don't see directly lifting the American Dragon into the WWE working. The Straight Edge messiah wasn't Punk's exact indy gimmick, but rather a modern re-imagining (he says so himself on his DVD, that a lot of his material is old material with a new approach instead of directly lifting it), Indy Punk was a scruffy kid cast away by society, whilst Straight edge society Punk was heavily inspired by Charles Manson with elements of his old character mixed in.As much as he's over now, I believe that if he used his American Dragon gimmick he'd get over even more. Look at punk, he's greatest work IMO was when he was the straight edge messiah, pretty much his exact gimmick in the indies. Part of that American Dragon gimmick was that theme and the way the crowd embraced it. I have no doubt the smarks in the crowd would make the casuals join in as well.
I'm much more for Bryan re-imagining and repackaging his indy persona to fit the WWE and WWE crowds rather than just rehashing old material straight off. Kinda like with Generico not handing over his mask I don't want to see Bryan try and re-do the American Dragon in the WWE only for it to fail, I'd much rather see a new character with elements of the old one in it.
As for the theme song itself. As I said before, it doesn't fit as a wrestling theme. All those other songs mentioned earlier in this thread fit well with the characters they belonged to. In what way does Final Countdown fit onto a scruffy, bearded grappler?
Long story short: I love Bryan's indy work, but I would rather see new material than just re-runs of his indy stuff. Just like I don't want to see Cesaro working a tag team with Ohno.