Change Journal (CJ) is used by the search engine to keep track of changes to the metadata. During an incremental update of the search index which can be triggered by the Administrator and when the search engine is turned off, it is therefore not capturing the real time update notifications.
Thus Quick Search (QS) has been designed to rely on Change Journaling and therefore disabling change journaling disables the Quick Search.
The current behavior is as follows:
Quick Search for Strategy Web is enabled at the server level via Strategy Intelligence Server Configuration > Web Quick Search > General:

Change Journaling is enabled at the project level via Project Configuration > Project Definition > Change Journaling:

For further information on the above access the help section in Desktop under System Administration > "Quick Search Manager" and "Enabling or disabling change journaling for a project source".
For more information on Web Quick Search, refer to TN41444 - New Quick Search feature in MicroStrategy 9.3.0 Web.