Earlier quoted context omitted.
Adding an empty alt tag is often the correct thing yes. Rule of thumb: if someone read the page out to you, would you prefer if they read that alt tag you are thinking of adding or not?
I wish omitting alt text was the equivalent of empty alt text. Nothing else works this way. If a page doesn't have a favicon, you don't add an empty icon href. I know empty alt text is preferred because otherwise, screen readers will usually revert to reading the file name. But I wish screen readers didn't do that.
You can though — it prevents a 404 error being logged in the browser console.
e.g.