If a person registers with a mask, will that have a significant negative impact on recognition either when person is wearing a mask or later when they are not wearing masks?

Registration with mask will have no negative impact on recognition with masks.  

When registering with a mask, only the masked face recognition model is created.  If recognition is attempted on a face that only has a masked face recognition model, then recognition will be attempted on the upper region of the face only.  

Note that mask detection must be enabled to perform registration or recognition with masks.