Is there a possibility to do this? I want to run a script that defines my network drivers and runs an .exe after it joined the domain.
You can redirect the default container of computers in your AD, and then apply there a GPO that runs a startup script.
After that you should move the new computer object somewhere else.
If moving the computer is not an option, you could make the script leave a semaphore file behind, so next time you'll be able to recognize in the script whether it already ran once.