Does an in-court-identification fall under the 'fruit of poisonous tree' doctrine when officers illegally detain a suspect?

When police officers detain a person, against his will,
 in a significant way so that he does not have the freedom to leave or move about they
have essentially arrested the person. In order for that arrest to be legal the officers
must have had enough evidence to equal probable cause. Normally, any evidence obtained
after an illegal arrest, and pursuant to that same arrest, is inadmissible in a court of
law. These are issues that the U. S. Supreme Court has examined for decades under the
protections of the 4th Amendment to the Constitution. The 4th Amendment protects our
interests in our "persons, houses, papers, and effects, from unreasonable searches and
seizures...." An arrest is a seizure; therefore, the 4th Amendment applies. If an
out-of-court identification is related to the illegal arrest, then, it would stand to
reason that the later in-court identification is the fruit of that illegal action.  If
the causal link is present, and no exception applies, the in-court identication is
analyzable under the fruit of the poisonous tree doctrine.