Is Ichigo technically dead? 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?
I would say yes.

It does not interfere with the "not letting the main character die" rule, because the main part of the story plays in the world of the dead (soul society). 

So I ask if the concept of "death and alive" even does apply to bleach? He might be dead ever since he first became a Shinigami or, as you described, as soon as his chain got destroyed. 

As for the time he is in his body and interacts with the world of the living, he might just go back into his body or as other Shinigami enter a Gigai (artificial body).

I sadly have no prove for this claim, it is my theory.