To be really useful, it would need to be able to communicate with something that is *inside* your network. If your router is capable of (and configured to) respond to a ping request, it would at least be able to tell you if either the router itself is down, or there is something wrong with the wiring between the router and the Internet.

If it were able to connect to a service on a computer inside your network, then it would be able to verify that the network upstream of the router is working as well.