How to attach new behavior to an AHAH button?

I'm trying to attach a new behavior to a submit button that already has AHAH behavior attached to it. This is what I have. If I bind a 'mouseover' event, it works, so I know the selector is correct.

Is it possible that since the AHAH will return FALSE, that any further click events will be ignored? Is there a way to attach further behavior to a button other than the default AHAH behavior defined by Drupal?

Drupal.behaviors.mediaAhahHideBrowser = function (context) {
  $('.media-browser-submit:not(.mediaAhahHideBrowser-processed)', context).addClass('mediaAhahHideBrowser-processed').bind('click', function () {
    // Hide the button.
    $(this).hide();
    // Next replace the browser with a progress indicator.
    // @TODO
  });
};