Sure, it can happen. Unlikely, but it can (why, b/c copper oxide is hard to ''stick'' to, try brazing dirty copper). Point is, it is accumulated for years. Worst comes to worst, melt the copper pan into an ingot and part it electrolytically 
However, that really doesn't happen because:
you don't need to incinerate to a ridiculously high temperature. It's all on how quick you want to remove the carbon. There's not too much reason to incinerate at brazing temperature (I'll call that 1600F, a good orange heat); it's just faster. I said to use Pyrex. The hottest you can really take Pyrex is about 650C which is more than enough to remove the carbon. You lose carbon quick enough at 400C.
As for stainless being used preferentially, I think it depends on the stainless. Some stainless will heat and age well (316 for instance), other stainless will flake off over time. As Harold said, quartz would be ideal.
Dissolution is something that has a different meaning to a lot of people. I routine use the term dissolve i.e. ''dissolve up the copper to leave the gold''. My idea of dissolving is to take something up into solution and have the option of either making it into something else or making it back into what it was.
Chris caught on instantly:
In the case of the filter paper, I don't really see it as dissolution because it's gone--you can't get it back, it is chemically destroyed beyond all hope of recovery. Whereas you dissolve gold, you can get it back by reducing it, or as Chris mentioned, boiling it down and decomposing it like this:
2 HAUCl4-->2 AuCl3 + 2 HCl -->2 Au + 3 Cl2
Really, this is about as close to disagreement as I come with anything I've ever seen Harold post and it's more me picking pepper than him being wrong. The cellulose does dissolve, but when it does it gets torn apart by the oxidizing and strong acid nature of conc. hot sulfuric.
However, that really doesn't happen because:
you don't need to incinerate to a ridiculously high temperature. It's all on how quick you want to remove the carbon. There's not too much reason to incinerate at brazing temperature (I'll call that 1600F, a good orange heat); it's just faster. I said to use Pyrex. The hottest you can really take Pyrex is about 650C which is more than enough to remove the carbon. You lose carbon quick enough at 400C.
As for stainless being used preferentially, I think it depends on the stainless. Some stainless will heat and age well (316 for instance), other stainless will flake off over time. As Harold said, quartz would be ideal.
Dissolution is something that has a different meaning to a lot of people. I routine use the term dissolve i.e. ''dissolve up the copper to leave the gold''. My idea of dissolving is to take something up into solution and have the option of either making it into something else or making it back into what it was.
Chris caught on instantly:
In the case of the filter paper, I don't really see it as dissolution because it's gone--you can't get it back, it is chemically destroyed beyond all hope of recovery. Whereas you dissolve gold, you can get it back by reducing it, or as Chris mentioned, boiling it down and decomposing it like this:
2 HAUCl4-->2 AuCl3 + 2 HCl -->2 Au + 3 Cl2
Really, this is about as close to disagreement as I come with anything I've ever seen Harold post and it's more me picking pepper than him being wrong. The cellulose does dissolve, but when it does it gets torn apart by the oxidizing and strong acid nature of conc. hot sulfuric.