I think it largely depends on how long AMD has been awesome. The argument that even if AMD was awesome, Intel would still come out ahead due to their huge profits advantage could very well be different.
Let's say AMD never lost its crown after the Athlon 64 era. Its processors have been consistently cheaper and better than Intel's processsors up until today. (or at least better after Intel was forced to eventually reduce prices) With AMD only on top during the Athlon 64 heyday, there wasn't enough time for AMD to gain a lot of ground on Intel's head-start (as a name, supplier to OEMs, money, etc). Athlon 64 certainly helped them, but Intel's name and connections were easily enough to carry them through that period unscathed.
Now if AMD had simply continued its reign since then, after another few years the status quo would have changed, possibly even flip-flopped. AMD would have slowly snowballed into being a true powerhouse, and who knows what would have happened. With this scenario, Intel's incredible profit lead over AMD would no longer be valid, as it would be an unknown. AMD could be the clear #1 processor company in the world, taking the spot that Intel used to hold years ago. AMD and Intel could be incredibly competitive and running consistently neck-and-neck. Or AMD could be much better off than they are now, but due to superior PR (as a whole) by Intel, or PR blunders (or lack of effort in this area) by AMD...Intel might still have a healthy overall advantage over AMD.
So yeah. I think the time that AMD has been awesome would be a huge factor. If they were awesome since Athlon 64, things would almost certainly be much different, possibly even in their favor. If they've only been awesome for the last few years...they would obviously be better off, but it would in my opinion merely be a repeat of the Athlon 64 days. Intel would still be the big bad giant it is today.