Is it possible in Spring MVC 4 return Boolean as JSON?

You can't return a primitive type (or a primitive wrapper type) and get JSON object as a response. You must return some object, for instance a Map or custom domain object.

The Map approach shown in your question is perfectly valid. If you want you can compact it into a nice one-liner by using Collections.singletonMap().

@RequestMapping
@ResponseBody
public Map<String, Boolean> admin() {
    return Collections.singletonMap("success", true);
}

You can't return a boolean, however, consider using ResponseEntities and use the HTTP status code to communicate success.

public ResponseEntity<String> admin() {
    if (isAdmin()) {
        return new ResponseEntity<String>(HttpStatus.OK);
    } else {
        return new ResponseEntity<String>(HttpStatus.FORBIDDEN);            
    }
}

This method will return an empty document, but you can control the status code (FORBIDDEN is only an example, you can then chose the status code that is more appropriate, e.g. NOT FOUND ?)