configure it to connect to an external full node. Is that possible?
Technically yes, but in practice, no.
bitcoin-cli connects to a
bitcoind via the RPC interface. This interface is typically not exposed to the internet nor are all IP addresses typically allowed to connect to it (specific IP addresses or CIDR blocks need to be explicitly allowed by the node operator). This connection limitation is because access to the RPC interface allows access to the wallet and can result in potential coin loss. Additionally, you will need to know the RPC username and password in order to connect.
So, in actuality, you probably won't find any
bitcoinds with open RPC interfaces that you can connect to, and since the interface is authenticated, you probably won't be able to connect to any node. You will need to have explicit permission from the node operator.