Filter Widget Defaults: How do I check to see if widget has a title?

As a designer, I want to “restructure” the widget output a bit to accommodate a design requirement and I know I can do this to some extent by filtering the widget defaults with this filter:

add_filter('register_sidebar_defaults','alter_widget_output');
function alter_widget_output( $defaults ) {

  $defaults['before_widget'] = '<div id="%1$s" class="widget %2$s"><div class="widget-wrap">';
  $defaults['before_title'] = '<h4 class="widgettitle">';
  $defaults['after_title'] = "</h4>\n";
  $defaults['after_widget'] = "</div>\n</div>\n";

  return $defaults;

}

However, in one case, I need to move the opening tag for the widget-wrap div AFTER the widget title so that the widget title is NOT within the widget-wrap like this:

function alter_widget_output( $defaults ) {

  $defaults['before_widget'] = '<div id="%1$s" class="widget %2$s">';
  $defaults['before_title'] = '<h4 class="widgettitle">';
  $defaults['after_title'] = "</h4>\n<div class="widget-wrap">\n";
  $defaults['after_widget'] = "</div>\n</div>\n";

  return $defaults;

}

The problem with this is that, when you do NOT provide a widget title for any given widget, you also lose the tag that opens the widget-wrap div :-/ Not good.

So my question is this… is there a template or conditional tag in WP that would allow me to check if a widget title has been specified so I could do something like this?

function alter_widget_output( $defaults ) {

  if($has_title) {
    $defaults['before_widget'] = '<div id="%1$s" class="widget %2$s">';
    $defaults['before_title'] = '<h4 class="widgettitle"><div class="widget-wrap">';
  } else {
    $defaults['before_widget'] = '<div id="%1$s" class="widget %2$s"><div class="widget-wrap">';
    $defaults['before_title'] = '<h4 class="widgettitle">';
  }
  $defaults['after_title'] = "</h4>\n";
  $defaults['after_widget'] = "</div>\n</div>\n";

  return $defaults;

}

Thanks in advance.