You did not indicate whether you're Master-Slave setup is synchronous or asynchronous, but yes, what you described should work. The slave should have a recovery.conf file and the presence of that will cause that slave to wind through all WAL files present before it resumes further processing. At least this is what happens in synchronous streaming mode. Your problem might be if the slave is off for an extended period of time or if one of the WAL files disappears. At that point the slave would not have all the transactions for consistency.
Again,to your question near the end. It depends on how you're set up. Generally though slaves do make the request to their master.