My extension uses an audio encoder (oggenc) and needs to know when the
encoder has finished and the file is ready.

I've managed it with shell scripts, but this is a very cumbersome
approach and requires different scripts on each platform.

So if I launched the encoder with nsiProcess, is there a way to
monitor when the process ends?

Yes, I know you can have nsiProcess halt the script and wait until the
process returns, but that causes the browser to freeze.