As far as I know, ADT will not allow you to do that.
This assumes you can even login into the panel to program the fire zone. If you can, then it would only alarm locally because ADT does not have the report codes for that zone at their central monitor station. When you call to try and add them, they are going to be like "Oh, hell no!" - That is not their equipment you are trying to add and you are in violation of their terms of service.

If ADT isn't getting paid and an ADT tech isn't installing, pretty sure it is a no-go on 'their' system.