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it does! ime it's a lot more practical to use a SNES Jr. and SGB for this in terms of just letting it sit on your desk (and it lets you customize the color palette to flesh tones and have a nice border that says "Pocket Camera"), but yeah i've definitely been joining dayjob calls with a GB Camera and a cheap ezcap dongle all pandemic long. (just be prepared for "oh, nice filter" remarks)
incidentally, in case you need a clean recording for demosceney purposes -- if you can get your hands on a GC broadband adapter, the homebrew GameBoyInterface can be used to serve a lossless APNG stream of the GBA's screen over the network, so you get a direct capture not subject to upscaling artifacts and TV signal chroma / capture device jank. (you might have to apply your own LCD ghosting in post, but that's a very simple ffmpeg filter)