No, was the instant response, but it'd be cool if they did.
While I'd be the first one to think that the planets with an outside would look cool if they did change with the time of day, I realize that TOR has bigger issues to worry about at the moment than background. Or weather, for that matter.
But something about that question did get me to thinking. Why is it that weather and times of day are simply bolt-ons to most MMOs? I say most, because the Tortage-at-night solo portion of the intro zone in Age of Conan does take advantage of the darkness to make it easier to hide, and that does carry over to the regular game.
Think of it this way: when was the last time that sneaking around in WoW was made easier due to cover or darkness? Shouldn't there --at the very least-- be a debuff or two associated with bad weather? I know I don't operate at peak performance in the rain, and there's the constant threat of hypothermia, so why doesn't your toon feel it? Shouldn't it take longer to trudge through a snowstorm or thunderstorm? If there can be a visible reaction to and a game changing debuffs associated with drinking to excess, why not with weather? Having a snowstorm or blizzard whip up, leaving your toon disoriented and weakened, would have an impact on whether you're actually out and about when the skies turn crappy. Hell, I'd have a harder time imagining that wandering monsters and intelligent opponents would be out in a downpour; you'd think that they'd confine themselves to shelter --makeshift or otherwise-- to wait out the bad weather.
Perhaps I'm taking realism a bit far, but I think it would make the sense of immersion that much more satisfying. In Ultima V, you could watch the shop keepers move around and back to their homes when night fell, so if a game from 1988 could figure such basic things as this out with the changing of the hours, then why can't an MMO do it?