You need to have field codes displayed in the document for Find to find a field. When you have field results displayed, you will get nothing found. That is, you need to be able to see the braces {} that are field delimiters. It is this first brace that Word's find is looking for.

Ignoring this formatting during printing will involve changing it. There is nothing you can click on to not print the underscore.

Rather than using direct formatting, you could create a character style with the characteristics you want. That way, to prepare it to print witohut those characteristics, you would only need to modify the style.