Disable all form elements when doing AJAX
Yes, it's possible. For example, you can attach a .js file to your form and extend the Drupal.ajax object.
Every element which can initiate AJAX submission from a form has its own instance of Drupal.ajax. You can find it in the global object Drupal.ajax. And every Drupal.ajax object has the methods success, error, beforeSend etc.
Here is a simple example to demonstrate the idea:


;(function($) {

  Drupal.testAjax = {
    // Our form
    form_id: 'node-type-form'  //Yes, I tested on my extended node creation form
  };

  Drupal.behaviors.testAjax = {
    attach: function(context, settings) {
      // We extend Drupal.ajax objects for all AJAX elements in our form 
      for (ajax_el in settings.ajax) {
        if (Drupal.ajax[ajax_el].element.form) {
          if (Drupal.ajax[ajax_el].element.form.id === Drupal.testAjax.form_id) {
            Drupal.ajax[ajax_el].beforeSubmit = Drupal.testAjax.beforeSubmit;
            Drupal.ajax[ajax_el].success = Drupal.testAjax.success;
            Drupal.ajax[ajax_el].error = Drupal.testAjax.error;
          }
        }
      }
    }   
  };

  // Disable form
  Drupal.testAjax.beforeSubmit = function (form_values, form, options) {
    $(form[0].elements).not(':disabled')
                       .addClass('test-ajax-disabled')
                       .attr('disabled', true);
  }

  // Enable form
  Drupal.testAjax.enableForm = function(form) {
    $(form).find('.test-ajax-disabled')
            .removeClass('test-ajax-disabled')
            .attr('disabled', false);

  }

  Drupal.testAjax.success = function (response, status) {
    Drupal.testAjax.enableForm(this.element.form);
    // Call original method with main functionality
    Drupal.ajax.prototype.success.call(this, response, status);
  }
  Drupal.testAjax.error = function (response, uri) {
    Drupal.testAjax.enableForm(this.element.form);
    // Call original method with main functionality
    Drupal.ajax.prototype.error.call(this, response, uri);
  }

})(jQuery);


This approach may seem a little difficult, but it gives you full control over AJAX in your forms.
Another way is to use jQuery methods like .ajaxStart(), because Drupal uses jQuery AJAX Framework.