I don't think they should for Skyrim/Xbox 360, for the simple fact it wouldn't work. Mods make the game highly unstable (at least in previous ES games). How would the 360 handle a crash? And SKSE (Skyrim Scirpt Extender
). I think it would be GOOD if they did that, but at the same time, i doubt it can be done. The 360 simply isn't designed for it. Except graphics enhancing mods, and even then, theres no knowing what that would do to it. And of course, theres the fact that a lot of content wouldn't be allowed to be downloaded on Xbox Live, because it would change the games ESRB rating. The reason it doesn't on PC, is because mods don't go through anything as official as Xbox Live.
Just my understanding of things, this could all be very wrong, just speculation