No. The story of Time and Darkness is quite literally the exact same as Sky, but less. Time/Darkness and Sky do not have the same relationship as, say, Ruby/Sapphire and Emerald, where the third game hashes both plots together with a little bit extra on top. Sky is the exact same story as Time/Darkness but with more minor plot points like Shaymin Village and Spinda Café, or fun side quests like the Special Episodes, and less variety of starters. I played Explorers of Darkness before I played Sky and there is nothing Time/Darkness have that Sky doesn't.
Do yourself a favour and replay Explorers of Sky. It is the best Pokémon game.