Question about User Synchronization plugin

I have a client who wants to have several sites one of which is a "Master" site. I see that the User Synchronization plugin will replicate user info from a master site to subsites. My client wants not only to sync the user info, but to set it up so that when a user logs in to the master site, they are automatically logged in to all the subsites. It does not appear that User Synchronization does that. In other words, I take it that the user data is replicated, but the user would still need to log in to each subsite, correct?

Assuming that's the case, I've seen some discussion of WP Multisite being able to do this, but it's not clear whether this requires additional plugins and/or code to make it happen. Anyone have any insight on that possibility?

Thanks in advance.