Not really.
You can do that with both rooted and non-root phones. Just one-click install all apps with the sync button on the top right or the “update all” button.
However, sometimes it fails and I need to install rest them manually if your phone is not rooted.
What is the installer method that you have selected?
Because all but root method will prompt me to install the app.
I’m using default session installer.
Edit: Just found something on their repository, they mentioned that they support one-click install, but in some conditions.
From https://github.com/NeoApplications/Neo-Store/issues/294
Simply put, it is normal that it sometimes pops up prompt window when user installing/upgrading some applications (because of having lower target api).