Thanks for your interest and question! Unfortunately, this plugin would not work for your scenario. It is designed to clone sites within a single multisite installation. However, that's a fairly common scenario and there are tools that can help you streamline that process (most of those are backup-restore solutions to move the data between servers or installations).
That said, depending on how familiar you are with source code management (SCM) solutions I'd recommend looking into something like Git or Mercurial. It takes a little bit of setting up but once everything is configured you can have a workflow like this:
1) Create a repository on your live site(s)
2) Clone / pull that repository onto your dev site
3) Configure the dev site to local settings (copy the db, update db connection settings, etc.) [This is only a one time thing unless you want to continually update / sync database content]
Then, you can branch the repository on dev and make updates / versions / patches / etc. When it's in a stable / releasable state on dev you can use Git (for example) to then push the updates to the master / source repository that's live. It's literally just a couple commands to create branches and deploy stable updates.
Here's a great article we've found useful:
Naturally, if you haven't worked with Git or SCM before and it's something you want to explore, you'll want to experiment with those scenarios completely offline on dev before you create a repository on your server. It's a really powerful solution once you get the hang of it.
But a backup-restore model is also valid as a manual and more straightforward approach. There are some really great back up everything in wordpress plugins out there to help streamline that.
Hope that helps!