Does a Na2SO3 solution oxidize to Na2SO4 in an oxygen rich atmosphere?
I'm not sure what is the stable form at room temperature, since we have both sodium sulfite ($\ce{Na2SO3}$) and sodium sulfate ($\ce{Na2SO4}$) in our lab and they're both stable, in air. I do know that the sulfite will oxidise to sulfate with the addition of bleach.

That said, your redox reaction is not quite accurate. In sulfite, sulfur is in the $\ce{S^4+}$ oxidation state. In sulfate, it is $\ce{S^6+}$. What happens in the reaction is that the sulfur gives away two electrons, which then go to an oxygen that changes from $\ce{O^0}$ to $\ce{O^2-}$.

One way of writing it would be $\ce{S^4+ + 1/2O2^0 -&gt; S^6+O2^2-}$. Total charge is preserved and there are no free electrons.