Content Connect is a Virtual Private Network (VPN) service providing the wireguard VPN protocol.
A Virtual Private Network (VPN) is a technology that allow your device to connect to another network and appear as if it is "physically" connected to that network (whether or not that network is in a different country).
The Content Connect apps implement the Wireguard VPN protocol which is a lightweight and simplified protocol. Being that it's lightweight battery usage should be minimal. But that being said you should expect to see all network activity registering battery usage time on your device as the traffic has to get routed through the VPN. So expect the Content Connect app to use a similar amount of battery as your device uses for WiFi or the mobile network connection.
The Content Connect app tunnels traffic between your device and the wider internet. So technically it will not use any more data then your device would've already used when accessing the internet.
Since the Content Connect service hides the internet sites/service you use from your Internet Service Provider if you are using service specific data bundles (like whatsapp bundles) you may not be able to access these internet sites/services as your ISP won't know that your device is trying to access those sites/services at that time.
To continue using this service specific data bundles you can exclude the apps you want to continue having access to from being routed through the Content Connect service. This feature is currently only available for Android users.
Being that each customer has their own Domain Name Server running on the same container that their Wireguard instance is running on users can then decide to "sinkhole" certain domains.
To sinkhole domains you basically keep the DNS from resolving queries for a set list of domains. The Content Connect service uses the Steven Black hostfile to determine which domains need to be sinkholed.