@Will Cho Simple answer is "No" OOTB. But there are ways you can implement this.
When a Pega Queue Processor is stopped, it stops processing messages from the queue, time to stop the queue processor depends on how large the queue is and how many partitions are present for that particular queue processor.
This can be done manually by an administrator or automatically as part of a scheduled job [ Job scheduler activity will be: pzStartStopQueueProcessor and, Parameters are QPName and QPStatus] or system shutdown.
When the queue processor is stopped, any messages that have not yet been processed will remain in the queue until the processor is started again. If the processor is stopped during the processing of a message, that message will be rolled back and returned to the queue to be processed again when the processor is restarted.