Is an evaluated function in Nashorn reusable from different threads?

Is it possible to reuse one and the same Nashorn engine and one and the same JavaScriptObject, which results as the evaluation of a JS-function, for all servlet requests, if the function does not change any shared object but uses only the arguments given with the call? Look at the following example:

public class MyServlet extends HttpServlet {

private ScriptEngineManager factory;
private ScriptEngine engine;
private ScriptObjectMirror script;

@Override
public void init() throws ServletException {
    try {
        factory = new ScriptEngineManager();
        engine = factory.getEngineByName("nashorn");
        script = (ScriptObjectMirror)engine.eval("function(writer) {writer.print('Hello, World!');}");
    } catch (ScriptException ex) {
        Logger.getLogger(MyServlet.class.getName()).log(Level.SEVERE, null, ex);
    }
}

@Override
public void doGet(HttpServletRequest req, HttpServletResponse res) throws IOException {
    try (PrintWriter writer = res.getWriter()) {
        script.call(null, writer);
        writer.close();
    } catch (IOException ex) {
        Logger.getLogger(MyServlet.class.getName()).log(Level.SEVERE, null, ex);
    }
}

Is this thread-safe? This is a follow-up to Reuse Nashorn ScriptEngine in Servlet