When Ichigo is being trained by Kisuke his second lesson involves Ichigo's Chain of Fate being cut, and in order for him to avoid becoming a Hollow he has to become a Soul Reaper.
After he gets out of the pit he was stuck in now with his own Soul Reaper Powers, Kisuke then begins his third lesson which is a fight. Between the start of the second lesson and the end of the third lesson there doesn't seem to be a point where they repair Ichigo's Chain of Fate (if it's even possible).
So is Ichigo technically dead because his Chain of Fate was cut?