Cloning is possible. You'll need to root and install custom recovery on every single one, do a nandroid backup of the original, and do a restore on the rest.
If all you need to do is clone the app and data, root all of them, install a root backup app, do a backup, then share the backup with all of them.
But if all you need to do is install the app on every device (no cloned data), just use an .apk extractor, upload the file to cloud storage (Dropbox, Drive, a website, whatever). You'll have to enable USB debugging on every device and allow installation from other sources, but at least you won't have to root 200 devices.
What exactly is it that you're trying to do? If we knew more, we could help you better. And maybe save you the trouble of doing something 200 times by yourself instead of 200 people doing one thing.