I've seem instances where ADT works with some home alarms and others where it does not.
This is true with any alarm company that uses VOiP. Several smaller companies work "hit or miss" with companies depending on the area that the house is. Why? I don't have the faintest idea.
Give a temporary number a try if you can with your ADT service for testing purposes. If it works, you have home service for $10. If it doesn't, you have 14 days to return the router with no questions asked.
No risk. No reward.