The nitric acid is HNO3 (not NHO3), yes you could dissolve most of the metals off of the melting the dish (that nitric can attack).
How well it would work to clean with acid would somewhat depend on how bad the dish was if the dish is heavily coated in base metal slag glass, you may not have much luck with acids.
An acid may not work well attacking this glass slag.
Even if you can clean a dish in an acid or wet solution the dish will soak up moisture, this moisture will have to be driven out of the dish before you get it hot again, even the little moisture a melting dish can absorb from sitting out in the air can break the dish when heated, if this moisture is not driven out, in preparing the dish for a melt.
Harold posted good instructions on cleaning the dish with borax, sodium carbonate (soda ash), and your torch, this way you melt and pour out most of the glass.
Melting dishes are very cheap just a couple of dollars, if I have a dirty dish I will clean it with soda ash and the torch, my older dishes get downgraded to melting the dirtier melts, my new dish is used for high grade melts.
I have never tried to clean a melting dish in acid, I use the torch with flux to clean the dish, and the dish gets downgraded in the job it is used for depending on the shape of the dish, if I need another dish I use one, I am very frugal and try to get the most use out of my tools, but when it comes to melting the gold, were you spend time and money on to get it pure, a new three dollar dish is very little cost to melt a couple of thousand dollars worth of gold in, and insure you are not contaminating the gold.
