Although AMS will provide a default set of dispatcher files for better security and performance of your website, you can always have a set of your own dispatcher files to add rules to them as per your requirement.
Most of the times, the websites will have their own set of dispatcher files on top of AMS provided files to manage specific requirement.
Contact AMS via ticket and they will provide you the detailed documentation of how to use dispatcher / add new files /edit rules / increase security etc.
So Vanity URLs and Redirects will work as it is as per AEM default functionalities in the AMS environment too.
https://helpx.adobe.com/in/experience-manager/kb/ams-dispatcher-manual/disp-vanity-url.html