Can a person still be considered competent after a sundown syndrome diagnosis?

Sundown syndrome and legal competence are two separate issues.  Sundown syndrome is not a diagnosis, but a number of symptoms often seen together associated with many brain diseases, but commonly associated with Alzheimer's and related disorders.  A sundown syndrome simply means that the person becomes more agitated, confused and upset late in the afternoon or early evening. 

Legal competence is a separate issue.  People may have a guardianship hearing to determine competence and that implies removal of their rights to make decisions regarding health or finances. Most daily life questions are actually about the individual's capacity to communicate related to a specific decision at one point in a progressive or worsening brain disease. 

Legal capacity includes the ability to communicate a consistent preference or value related to the decision.  If someone with moderate stage dementia exhibits sundown symptoms, s/he may still have the capacity to express preferences or values related to a specific decision, even if making the decision or understanding the full consequences of the decision are beyond his/her capacity.  You would need to know competence or capacity "for what?", regardless of the presence of sundown syndrome.