App Manager is not a firewall app. It does not prevent an app from phoning home (or to any other offensive sites). It can block components which may be used to monitor the behaviour of a user, collect data, display advertisements or prevent working with other offensive apps such as Google Play Services (GMS) to track users. Since they consume a lot of power, blocking them would not only reduce data collection but also make the device a lot more faster. So, for a complete privacy, you should also use DNS- or VPN-based firewalls to avoid phoning home. (However, you should avoid apps that directly modifies the ip-tables because it's unsafe and UID-based blocking is not a good firewall in Android.)
Anyway, if your OS allows it, you can completely block internet connections for an app using App Manager via net policy.