Yes, the WAVE Chrome extension can be used to inspect HTML files on a local desktop server.
Simply click the WAVE extension icon when your webpage is open in Chrome on either localhost or 127.0.0.1.
It will scan the page and highlight accessibility issues directly in your browser.
This keeps your stuff secret and functions even without an internet connection.
However, local or localhost files cannot be accessed by the WAVE online tool (wave.webaim.org).
It only works with publicly available URLs.
You would need to use technologies like ngrok to expose your local server if you wanted to test a local site using the online tool.
For local development, the Chrome extension is the most convenient and effective option.