That's how I read it as well. Either Kaladin's forced use of stormlight broke Syl, or Syl died as her last act to save Kaladin from his fall.
Honestly, I found Kaladin's constant gloom off-putting. He went through an entire character arc in WoK, and finally learned to trust Lighteyes, only to fall completely back into his old ways and completely ignore Syl? I understand what Brandon was doing, but it was a tough read.