Does snaking a shower drain resolve a leak?
No. A clog doesn't necessarily result in a leak (usually doesn't, in fact), and there should be no water in the downstairs ceiling. 

You have two distinct issues here, or possibly a complex issue involving both a clog and a leak. Were it my home I'd open the relevant areas and find the true cause of the problem.


  Fixing the clog might mask the leak, however, and make it less
  apparent. When the pipe is full of water, water was apparently
  streaming out of the leak into the neighbor's unit below, but now that
  it's fixed, the water may merely be dripping out, making his ceiling
  wet, but not enough to notice... until the mold sets in. So it's still
  a problem, but now it's a hidden problem. ~Johnny