Never gonna happen for several reasons. First, for all of the reasons that Brad Humphrey brings up. To report a Fire Event then a zone must be setup as a Fire Zone. Unless their ADT system already includes some Smoke Detectors then there won't be a Fire Zone set up.

Second, the Nest is not a Smoke Detector, it is a Smoke Alarm (there is a difference). Although Kidde and other brands (and I doubt Nest) make relays that take the signal wire (Does Nest even use one or is it Wi-Fi?) from a 120 VAC Smoke Alarm and convert it into a contact closure, these relays are not code approved for tying the Smoke Alarm into a Fire Zone on a Fire Alarm System. They are designed for adding additional sounding devices or strobe lights etc.