Q: Can Activity Monitor connect to the computers through the Internet?
Basically it can, but there are certain limitations. You need direct IP connection between computers, proxy servers are not supported. You should be able to ping the remote computer. Also it's desirable that both computers have static IP addresses. You may install Agent remotely only if you know local Administrator password for that computer. Monitoring will not be fast on slow Internet connection as Activity Monitor is designed for using on LAN.
If you need to monitor your remote office, that has own LAN with multiple computers, we recommend a solution using Windows Remote Desktop Connection. Install Activity Monitor on one of the computers in remote office. Connect to that computer via Remote Desktop and monitor computers on that LAN as if you were sitting there.
We recommend using VPN connection for monitoring computers outside your LAN