I thought about it (more out of curiosity than interest in actually trying it). The big obstacle I see is that the Sodastream bottles are designed to screw onto the carbonator. I don't think you'd get a good seal on a beer bottle, and you'd end up just wasting a lot of co2. Even if you could carb it, consistency would be very difficult.
If you tried it I'd be interested to hear how it turned out.