In the Bleach manga, does Byakuya really die in Bleach 502?
You should probably just live with the dramatic tension as you keep reading through the series.  That being said...

The short answer:


   He gets better.


The slightly longer answer:


   He gets better.  And gets a power-up.


The longer, more detailed answer:


   He hangs on by a thread.  And then Squad Zero--recall we heard about them during the Turn Back The Pendulum arc--shows up when the Quincies leave.  One of them takes Byakuya and a few others with them up to the Royal Palace.  Byakuya and a few others then get healed up, equipped, and trained in the Royal Palace.


I left a fair amount of details out of the above, so some things won't be spoiled, but it still spoils a fair amount even in its vague brevity.