Seems like to me, the OP has an alarm system (ADT) that is functional outside of ST and wants to bring in those sensors into ST…Meaning, keep his current alarm system AND incorporate the sensors into ST…
The OP’s question is the exact question I had when faced with the same scenario. Of course someone immediately said it could not be accomplished. However, there is a 3rd party device called Envisalink 4 that I was able to purchase for about $80 that allowed me to interface my alarm system into ST using a community created App and DTH(s) called Alarm Server. Doing this, I also gained 28 sensors that I was able to use in other Home Automation scenarios.
Similar projects have been done for ADT Systems as well. Here is one for example:
As JD explained, it really depends on what equipment the OP has.
Saying no without actually having the proper information needed in order to give a qualified answer is, IMHO, a disservice.
Finally, I had absolutely no technical know-how to do all the things that I have accomplished with my current HA system. However, this community Rocks! There are many users willing to walk users through seemingly difficult setups. Now, what once seemed super overwhelming when I first started off, is now walks in the park. YMMV