Are there any other ways the 3gig gc2 unit can send notifications? To my Z-wave controller?
The 2GIG Panel is designed for use with one of a few different back-end service providers, as a dedicated alarm unit.
Alarm.com is one of the providers and an Alarm.com communication module would be needed in order for it to communicate. To use an existing 2GIG Panel with suretyDIY service, this page goes over everything you might need.
If you are trying to use the 2GIG Panel without service, there will be extremely limited functionality as it is not intended for use in that way. It can work as a local noisemaker, or you might integrate it with another system, although there is still very limited functionality.
Z-wave in the 2GIG panel does not affect the Alarm or arming state, although you can trigger a compatible Z-wave device when an alarm occurs. For more information, see this post.