Is an external GPU possible for MacBook Air 2012?
For macOS Sierra or earlier, you can use automate-eGPU.sh to enable your eGPU.

For macOS High Sierra or later, you will require purge-wrangler.sh to get your eGPU up and running.

Regardless of a high success rate of these workarounds, it is recommended that you purchase an eGPU setup you can return for a full refund in case things don't work out.