Oh, sure they would. Throw a bottle of cleaner in a 1/2 tank (or whatever the label says on the cat cleaner you buy, you'll have to look up your fuel tank's capacity and get the ratio right). Easy peasy. Do it again yearly or when the code crops back up.

If you want to go full DIY, you can get a cheap (~$25) Bluetooth-enabled scanner like https://www.amazon.com/dp/B073XKQQQW that plugs into the car's OBD2 port under the dash - any free scanner app will tell you what the code is that turned on the engine light. P0420 to PO424 and PO430-PO434 are catalytic converter codes. When you get one of these, dump a bottle of cleaner in your gas.

This is what the shop is charging you $175 for - plugging their fancier scanner into your car and reading the codes.