Of course you do, the whole GSX runs inside of it. Not sure why you titled this "Coautl vs FSDT installer", as if they were similar or doing similar things:
- The FSDT Installer is just an installer and an updater
- The Couatl .exe is a Python interpreter that runs alongside MSFS to run the GSX code, which is written in Python.
Of course, if you were more precise about your issue, we could possibly know why the program doesn't start anymore. The Sticky thread here would help:
http://www.fsdreamteam.com/forum/index.php/topic,26759.0.html