There are several considerations to keep in mind and different setups that could help you with your proposes.
1. The alerts are executed by the Pandora FMS server, not by the agents.
2. If you make a local installation of Pandora FMS and you only have 1 internet access (only 1 public IP), you can monitor that you don't have internet access, but you won't receive the email, since it is not possible to send it from a place that has no internet. So you would either need two internet accesses on that office, or a different alerting system like SMS.
3. If you make a cloud installation of Pandora FMS you can monitor the internet access of you offices in two different ways: first you can execute a ping against the public IP of your office, if it doesn't respond, then that office has no internet access; second you can install an agent inside of the office, if the internet goes down the agent WON'T be able to display a critical status since it won't be able to communicate with pandora server, and pandora server would display an "unknown" status, meaning connection with that agent is lost, so most likely internet is down. Combining these two options may be the best solution I think.
I hope this helps.