If by 'originally' you mean since the very first draft, no. The earliest draft has General Luke Skywalker as an aging Jedi Master, while Anakin Starkiller is his apprentice. Annikin has a father, Kane Starkiller, and a brother, Deak Starkiller, who is killed by Vader early in the film. The Starkillers live on Utapau (which would eventually appear in Revenge of the Sith). Princess Leia, on the other hand, is the biological daughter of King Kayos and Queen Breha of Aquilae. Her brothers in this draft are Biggs and Windom.
In the second draft, Princess Leia has little more than a cameo. The biography "The Cinema of George Lucas" describes Leia as the niece of Owen and his wife Beru, and the sister to Biggs, Windy, and Luke, who live on the planet Utapau. Deak Starkiller is not killed. Instead, he is the character held captive by the Empire. General Luke Skywalker and Annikin Starkiller have been merged into a single character, Luke Starkiller. Biggs and Windy are now the youngest of the Starkiller siblings. Their father is simply known as Starkiller. The droids find Owen, having been instructed by Deak that he will lead them to "Angel Blue" (Luke Starkiller). The most interesting note about this draft is that it is Luke's brother who takes Leia's place as the Empire's captive. It would seem at this point that Leia had become Luke's sister; however, by the followng draft, this would be reversed again. (Interestingly, in the book "The Making of Star Wars: The Definitive Story Behind the Original Film," this draft is described with an important difference: Leia is named as Luke's cousin. Therefore, her role in the second draft is not completely certain.)
In the third draft Leia is from Ogana Major, and from all indications she is the biological daughter of their royal family. In the fourth draft, Ogana Major became Alderaan, and a slightly modified version of the original planet name, "Organa," became Leia's last name.
The first draft of The Empire Strikes Back features a brief appearance by the ghost of Luke's father, who tells Luke that he has a sister who is undergoing Jedi training on the other side of the galaxy. Based on this description, the sister in question is clearly not Leia.
At one point, Lucas claims to have considered making the principal character a female (some early production art reflects this direction) but eventually decided to keep both "versions" of the character as siblings.