It is appropriate only if the added fields have sense (and are coherent) for the type of the exception, and especially if these informations are useful to better understand the cause of the exception.
Take for example the java.text.ParseException that has an errorOffset information or the org.xml.sax.SAXParseException that can give infos about lineNumber, columnNumber.
You should not use exceptions only to "pass" something to other parts of your software, just because it is convenient.