You can get selected text using the context menu. In your background script, adding these lines will allow the user to right-click and do something with the selectionText.
chrome.contextMenus.create({id:"lookup",title:"Lookup %s",contexts:["selection"]});
chrome.contextMenus.onClicked.addListener(function(sel){
console.log(sel.selectionText);
});
Grabbing this text works fine with PDFs, whether part of the extension, or not.
However, you cannot inject a script into a page starting with "chrome-extension://". If this is how your extension works, that will not be (directly) possible. But getting the selected text, and doing something with it still very doable.
As an alternative to requiring script injection, see the notification api, which allows a small message to popup, which could contain the definition of the word.