Will this reaction occur?
But I thought why not $\ce{SO2}$


While the reaction is stechiometrically correct, it is hard to perform.


In excess of $\ce{H2S}$ sulfur will be produced.
In excess of oxidant sulfate will be produced.


And exact balance is impossible to achieve.

That said, $\ce{SO2}$ reacts with  $\ce{H2S}$ finally producing sulfur. This reaction, just like many inorganic reactions, is an unholy mess of many different processes with many products obtained simulationaly and the only way to produce understandable and reproduceable results is to simplify the situation. One of the way to simplify the situation is to use a vast excess of one of the reagents.