Ok, there’s cheap, and then there’s, um, makers. LOL! 
Sure, if it’s only one sensor you can connect it to anything you can cobble together that will be recognized as a detectable device in smartthings, and you might be able to save some money that way.
I would look into ST_anything using an arduino and an ESP 8266 as one possible do it yourself option. (The topic title is a clickable link)
@ogiewon might have some more thoughts.
If you want to go even simpler, look for some physical event that occurs when your ADT system is triggered, whether it’s a light coming on or an LED changing color or a sound and then just find a sensor that can recognize that.
For example, here’s a sensor designed to trigger when a small indicator LED changes:
But there are lots of other devices you can use depending on the exact details of what changes in the physical environment. 