Yes, ADT Provides the monitoring, but the only devices which are allowed to send a notification to the central monitoring system are the dual logo devices (Which have both ADT and SmartThings logos on the box). And again, those are using a completely different proprietary communication protocol which will work even if your power and your Internet are down.
You can integrate your other devices with your ADT/SmartThings panel, but only for home automation purposes. Those devices are not allowed to trigger notifications to the monitoring center because they are not considered reliable enough.
You can talk to people who are actually using the system in the following thread ( this is a clickable link)