Is Ichigo technically dead?
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.