Quiescing and stream server are two completely different concepts. Stream server is needed  to support queue processor (among others), which is the long term replacement of agents for background processing. See this link for some common questions regarding queue processor: https://community.pega.com/knowledgebase/queue-processor-faq.

Quiescing, on the other hand, is to save requestors to database so that they can be activated later as need - mainly for high availability. For example, if you shutdown one node (gracefully), Pega will save all the current requestors to database automatically so that the end users will not notice any difference as their sessions will be moved to another active node seamlessly - quiescing makes that possible.