No, a PageReference isn't content, it's just a reference to some content, which Visualforce then redirects the user to. You could render your json in a Visualforce page and specify the mime type, for example:
<apex:page applyHtmlTag="false" showHeader="false" contentType="application/json"
However, if you need to return JSON or XML in this manner, you would probably be better off using Apex REST to write a class that handles HTTP requests & responses directly, without invoking Visualforce. And since Apex REST exposes your class at a public URL, you can always return a PageReference to the URL from your controller if you have a use case that does require redirecting from a VF page to an API end point.