If you want to send an email, you have some options:
-Use a GSM module, and rely on outbound SMS or 'calls' (That function like a modem) to connect to a 'gateway' that will convert the SMS or 'call' to an email. The gateway will then send the Email on the device's behalf.
-Use a GSM module that supports data so that you can send an email directly from the device. (This method will still require that the device is configured to use an outbound mail provider, and will usually require a data plan from the mobile provider)
-Use WiFi, and hope that it finds an open access point. (Not ideal!)
There are other solutions that rely on radio, but would be far too costly to setup. All of the work is taken care of already with cell towers, stick to that.