Yes. This is included in packages with "custom icon".
Not all features of Personory are found on this web site, so please, take a moment and ask if we support or offer a given functionality you need. If we don't, we will discuss it with you and see about adding it into Personory.
Like all features of Personory, you can disable/enable given features. So you may wish to leave the map enabled for the admin user, but disable the map for everyone else.