Hello,
UPDATE: phpdocx 9.5 added support for custom character styles when importing HTML.
No, there isn't support of Word character styles when importing HTML; you need to add them setting strictWordStyles as false and through HTML styles; or don't use HTML content but native methods: addList, addText, WordFragments...
It's explained on the documentation pages:
'One may use native Word styles for paragraphs and tables.'
To set span styles you need to set strictWordStyles as false and add the styles inline or through CSS. If some styles aren't applied then they're not supported.
Regards.