I would like to use the GL2 to simultaneously record while outputting via firewire (to stream the recording live). Can the GL2 do this?

Yes. That's basically how direct-to-disk devices like the Firestores operate.

You can also output it to a PC that is running a Capture program. I do this with Sony's Vegas Capture.

I found that I had to change the setting so that the camera would stop rather than shut down after not doing anything for a while.