Right. They’re not going to see the login form.
Yes, but they won’t automatically appear on the user card, which is where you want the data displayed right? Nevertheless, if that’s what you want, you can just add any arbitrary field in the wpdc_sso_params filter, e.g.
$sso_params["custom.not_a_user_field"] = "field value";
This will be stored in Discourse in the user_custom_fields database table, but won’t be visible anywhere. You can query it using the Data Explorer Plugin.