Yes, you would have to make this change directly to the database. You would also have to make sure that the converted text is according to the XML text field standard.
To do this you need to change data in the table ezcontentobject_attribute. You need to make sure that you only update rows where the field contentclassattribute_id has the correct id. Valid XML data in the data_text field there can look like:
<?xml version="1.0" encoding="UTF-8"?>
<section xmlns:image="http://ez.no/namespaces/ezpublish3/image/"
xmlns:xhtml="http://ez.no/namespaces/ezpublish3/xhtml/"
xmlns:custom="http://ez.no/namespaces/ezpublish3/custom/">
<paragraph>This is some plain text in a paragraph</paragraph>
</section>
Then you need to change the data_type_string to ezxmltext in both ezcontentclass_attribute and ezcontentobject_attribute.
Remember to do a backup before you start testing this.