Large Sleep counts causing THREADPOOL wait?
What I really want to know is do sleeping sessions hold a thread? 


No, they do not, 


  A SQL Server worker thread, also known as worker or thread, is a
  logical representation of an operating system thread. When executing
  serial requests, the SQL Server Database Engine will spawn a worker to
  execute the active task. 


But instead of actually spawning a new worker, one is typicall available in a pool


  The max worker threads option enables SQL Server to create a pool of
  worker threads to service a larger number of query requests, which
  improves performance.


Thread and Task Architecture Guide -- SQL Server task scheduling

which you can see from running

select count(*)
from sys.dm_os_workers

select count(*)
from sys.dm_exec_sessions


Since you typically have more sessions than workers.