Yes.... You can put other things besides strings into JOptionPanes.Such as you can put a JEditorPane that displays some HTML, which can in turn have links in it. Or buttons that look like links.
But I've also had problems in modal dialogs in some cases where clicking the links in HTML doesn't work correctly (the HyperTextEvent doesn't get fired).
As for same effect... Well, it's usually more complicated than that. Applets are simple (Applet.showDocument(), or AppletContext, whatever it is). Otherwise you need to do something different. Search the forums for posts on launching URLs from applications, there's plenty o' info.