I feel like this could work quite well. Aside from the prequels, the series has a very retro vibe to it anyway. I wouldn't have any issues with a film being presented to look like it was actually made on analogue technology. In fact, I think it'd go hand-in-hand with the found footage genre and that's something else I think Alien is quite suited to with the helmet cams in Alien and Aliens.
I think it might be something better done with fanfilm or things like the Tongal shorts (and I'm surprised no-one has really done a found-footage fanfilm) than a theatrical release, but I do think it'd work and wouldn't feel out of place.