No. That's the reason why sf::Sprite and sf::Image are two separate classes.
sf::Image is the heavy one that holds the pixels in memory, and sf::Sprite is just a lightweight interface that describes how to draw an image. All it does is to store a pointer to the sf::Image that you give it, it doesn't copy the pixels. This way, there's no unnecessary overhead if you want to draw 1000 sprites that use the same source image.