Can I convert from an emission amount (in tonnes per area) to a concentration (in ppbv)?
What you are doing seems reasonable but there are many hidden assumptions in your technique:


The data source you are using actually provides a rate, i.e. metric tons per area per year.
Thus your calculation is also implicitly a rate: the results will be in tons per volume per year.  
You are assuming that the only source of atmospheric $\ce{SO2}$ is the emissions quantified by your data source.  It may well be that there are other, natural sources of $\ce{SO2}$, or more likely, natural sinks of $\ce{SO2}$.
If you want to know actual concentrations, you will need to quantify all the other sources and sinks of $\ce{SO2}$, and integrate all sources and sinks over time.