Is it true hurricanes and other large storms clean the air?

I don’t know much about hurricanes, specifically, but storms (those with lightning, in particular) ionize the air. Pollutants tend to be positively charged particles, but the increase of negative ions in the air created by storms will attract the pollutants and they then “stick” together, and ultimately become more dense and will no longer float. They get washed down with the rain.
When you add an electrical charge, such as with lightning, it breaks apart regular oxygen and some will reattach with an additional molecule and ozone is created. Ozone is then made up of three oxygen molecules and is a powerful oxidizing agent, and while it may not be ideal for breathing, it is beneficial in neutralizing (other) pollutants and when it comes in contact with a contaminant molecule it will oxidize and destroy that other molecule (along with the additional oxygen molecule), and the result is pure oxygen (O2). Ozone is also used in some places to disinfect in hospitals and other industries, in place of bleach, and I have even heard of it being used to decontaminate water supplies. It’s harmful to us to be exposed to large amounts of ozone, but it is more or less “nature’s disinfectant.” That is why the air smells so fresh and wonderful after a good storm, the air is charged up and loaded with fresh oxygen.
So, the air is most likely being “cleaned” by a good storm, but what happens to the contaminants depends a bit on what’s going on in the sky. Not 100% on all of this, I’ve been out of school for a long time and I’m feeling like I’m forgetting stuff, so hopefully if I’ve missed anything or if I’m wrong about parts of the process someone else will come along and fill in my gaps. Rough idea, though.

I would be more concerned about the ground and water pollution the storms can cause, honestly.

Well they sure wash the dust and pollen out of the trees over here, which is great for me and my evil allergies.
As long as the air is cleaned within 100 feet over my head I’m happy with that. haha

They also housekeep all the dead wood, broken limbs, and weak roots in the woods.