Yes, but taking a "working" reference from "more info and pasting it into info is the easy part From incl/modules/sideboxes/more_information.php and adding to incl/modules/sideboxes/information.php

Code:
  if (DEFINE_PAGE_4_STATUS <= 1) {
    $more_information[] = '<a href="' . zen_href_link(FILENAME_PAGE_4) . '">' . BOX_INFORMATION_PAGE_4 . '</a>';
  }
Slight edit to correct the sidebox required