After finding out info from this blog, it seems like there is indeed a way to make Fraps register AO and AE - But it's a little complex. I used my old 17" TFT monitor for this - Not sure if you can make a widescreen monitor run at 1280x1024.
You have to use DxWind and configure that to run AO at 1280x1024 in a way that doesn't show a window border, then wrestle with your mouse to centre the window on your screen. Set up Fraps to record the desktop (Monitor Aero Desktop), and there you go. It's a little choppy in parts though and doesn't do the FMVs very well.
I was going to do a walkthrough of AO, but realised just how pointless that would be. This was to be the first part until I decided not to bother doing it anymore. Instead this will simply be a quality demo of Frapsing AO - Even if YouTube loves to corrupt my vids for some reason.