The default Members field ("assignments") includes "complete" state when returned from the API. Custom Members fields only return userIds for those users assigned to that field.

However, all Members fields can have their "complete" status set via both the API and GUI.

The GUI displays a Card as "complete" if Members fields have that field marked as complete.

Therefore, Favro must be storing completion state for all Custom Member fields. Since the API does not return this information, there is no way to use the API to check for completion state of either a specific Custom Field or the full Card.