drupal_render in hook_form_alter prevents javascript from being included in the header
Setting the #id to $wrapper['#id'] = drupal_html_id('edit-' . str_replace('_', '-', $wrapper_field_name));  resolved the issue.  theme_textarea was unable to get a value for $element['#id'].

edit

I still had trouble getting the #ajax elements to be processed even after adding a call to ajax_pre_render_element.

I restructured my alter hook so that it prints the textarea inside the form element that I'm trying to append to. that way it prints both fields one after the other.  This way, I'm not touching drupal_render and everything works.