Handling of emphasized text is hard-coded in org-element.el. Unfortunaly fixing this requires more than teaching `org-element-text-markup-successor' about `org-emphasis-alist' because separate `org-element-TYPE-{parser,interpreter} functions are used for each type of emphasized text.
Wouldn't it be better if bold, underline, ... would all use the same parser and interpreter? I don't see another option that would allow custom emphasize styles to be used with org-element. Thanks, Jonas