Since A2:PMC, it's possible to run videos in game via the OGV format. There were some early teething problems with playback on certain hardware, which were addressed in a subsequent patch or two.
They're a nice addition/ option to have, but - particularly in full-screen - their quality can suffer when trying to balance resolution and filesize. Dark scenes particularly can suffer. I find that they're best deployed as smaller resources, such as the small "video feeds", etc; although, fairly long full-screen footage can work nicely, if your players are willing to download the extra data. For example, the 'title screens' for each showcase were OGV videos running in fullscreen. I think they're only ~5-10MB each, and are 10s long.
I believe that the OGV playback doesn't handle alpha (at least in our current implementation), so you will always end up with the black scene, even if you export with an alpha channel, capturing the footage as you describe above.
You can, actually, play image sequences already though. It's a bit of a hack, but if you were to export your composition as a png-sequence with alpha, a simple script can play this back, calling the numbered images at whatever framerate you've exported it in. We actually used this 'hack' in the E3 presentation in our prototype of the context-hint system, found in the 'Deterrence' mission (such as fire support), which is actually a sequence of 90 images, called by script.
The problem here again is the data size. In my example, it was only a very small image for 3 seconds, but we're still talking about loading and scrapping a lot of data, and I'd be concerned about performance when trying to do anything more complex/ longer/ fullscreen. It's not engine supported, nor is support for it planned at the moment. As long as Ondra (or anyone else that may explode over a 'hacked' 'designer's' 'implementation'™) doesn't see it, you'll be fine.
If you carry out any experiment in full-screen, for example, perhaps overlaying some png-sequence of particle effects on a real-time rendered scene, that'd be fascinating to see in action!
Hope that helps!