If I add an user in the admin console and then provide permission to that user to access the AEM instance, that gets auto synced to AEM. But, if I update permissions for the same user in the AEM instance, will that reflect automatically in the Admin Console?
What do you mean when you write "permission"? The Adobe AdminConsole does not now about any permissions, but just knows users and groups and their relations (next to some other things, which are not significant for this question).
The only direction in which there is a sync is from AdminConsole to AEM. That means that any user-to-group relationship visible in the AdminConsole is synced into AEM, but not the other way around.
When referring to "permission" in the context of AEM, we normally mean the permission to access nodes/resources in the AEM content repository. This is entirely handled within AEM itself, because the AdminConsole does not understand this concept at all. Typically these permissions are mapped to AEM groups, and these groups can be handled within the AdminConsole as opaque entities.