I was wondering if it would be possible to write a file, not to the local system, but to a connected server or other network path.
Would I have to use an external interface for this or can I entrust this to the AIR framework?
I'm pretty sure that AIR has certain security precautions to prevent this.
What kind of network path? SMB, FTP, HTTP, WebDav, .. ?
If it's mounted on your local PC, then you should be able to write to it just like writing to any other drive or filesystem.