No, there's no simple relationship between NOx and HC. Lowering peak flame front temperature by retarding timing will reduce NOx, without much effect on engine out HC since engine out HC is primarily a function of A/F ratio and design issues such as quench area.

So lets take the A/F ratio out of the equation by assuming that the lambda system is operating properly and maintaining stoichiometry. Retarding the timing under any engine operating condition will reduce peak flame front temperataure, which will generate less NOx, and reduced timing will also increase EGT, which will increase converter temperature. So you end up with lower engine out NOx, about the same engine out HC and CO, but since the converter is hotter both its oxidation and reduction efficiency increases, which should lower all emissions at the tail pipe.

For a loaded test that measures NOx, the parameter that tells you how well the converter is operating is O2 content. If it measures zero, the converter is operating at or near peak efficiency. If it more than zero, it is not - probably because it is too cold - and this will usually show up as high HC - often near or over the test limit.

I retarded my timing map to reduce HC, which is the result I got - lower HC and reduction of O2 content from 0.1% to 0.0%, which meant the converter was operating at higher efficiency. I also expected to reduce NOx, but the 90 percent reduction really surprised me, and most of that reduction was likely in the flame front (lower engine out NOx), not due to better converter efficiency though it probably helped.

http://www.peachparts.com/shopforum/showthread.php?p=833484#post833484

Duke