Release of sulfur dioxide from odored fuel gases
According to this North American Energy standards board publication , the total concentration of sulfur in natural gas, both natural and from oderant additives, must not exceed $\pu{70 ppbv}$. Concentrations are actually more commonly about a tenth of this. For example, from the same source, the Union Gas system typically contains about $\pu{5 ppbv}$ sulfur.  Furthermore, the sulfur content of coal is many orders of magnitude higher than that of oderant-enriched natural gas at about $\pu{0.5 to 5\%}$ sulfur, and the worldwide combustion of coal is much greater than that of natural gas (although much of the sulfur from coal combustion is now scrubbed out at the source of combustion). Other fossil fuels like diesel also contain significant amounts of sulfur (regulatory sulfur content of diesel fuel in the US and EU was 10 ppm as of 2009).

The global atmospheric background concentration of $\ce{SO2}$, according to 
Owen, Lewis A.; Pickering, Kevin T (1997). An Introduction to Global Environmental Issues. Taylor &amp; Francis. pp. 33–. ISBN 978-0-203-97400-1, is around $\pu{1 ppbv}$, meaning the sulfur content of the Union Gas product, for example, is only five times that that found throughout the Earth's atmosphere.  

Summary - TL/DR:
Based on the background $\ce{SO2}$ concentration and the overwhelming sulfur emision source from the combustion of coal and other fossil fuels, the sulfur originating from natural gas oderant additives represents a negligible contribution to the global atmospheric $\ce{SO2}$ concentration.