I was also thinking on a video recorder, but thought it wouldn't be possible, at least not on an o3DS.
The concept itself would be possible, in fact Roller Coaster Tycoon 3 takes its videos in a similar way (by taking frame by frame screenshots.) The issue is getting sound (which may not be possible), and figuring out a way to even automate the screenshotting in the first place (also maybe not possible).
You'll just have to wait a pretty long time... a screenshot takes what, a second or two? Let's say you skip every other frame and make it a 30fps video, that's 30 or so seconds per second of video, so for an average 3 minute Smash replay that'd be 1.5 hours. So it'd be an overnight type of deal for something like a full Pokemon battle video, and definitely couldn't be used for anything other than replays.
EDIT: Not to mention there's no way in hell it could encode on the fly, these times are basically if you dump the frame buffer straight to file and then convert later. So it's really almost not worth it, more of a proof of concept that I wanted to try and implement. Best case scenario, let's say you make it 24fps and then assume that only capturing the top screen takes half a second, you'd get probably get a max of 5min/hr vs 2min/hr, which is still pretty damn slow.