I kinda brought up that point before, only without the romantic/sexual connotations.
But yeah, despite being a goddess, I doubt Shulk would want to take her out for any reason. Rosalina isn't like most gods in games. She started out completely human, and through some as of yet unexplained circumstances, obtained her great power. Since she was once human, and possibly gained these powers against her will or knowledge, she's not power hungry at all and doesn't actually abuse her powers. The universe is her child as much as the Lumas are, and while she guides it and wants it to prosper, she wants it to make it's own decisions, like any good mother would allow their child. So there is no reason for Shulk to want to be rid of her, from what I know of him. Also, from what I gather, he likes reading, and Rosalina writes stories, so there ya go!
She never outright says "I'm omniscient", but she somehow knew about the entirety of events in Galaxy 2 (the game is a story she is reading to the Lumas - this is revealed in the 120 Star Ending). However, she only appears in the regular ending before that, and leaves very swiftly.
And the definitive proof that the story of Galaxy 2 did happen, and wasn't just a story she wrote, lies in the fact that in the regular ending, Young Master Luma takes Mario's/Luigi's hat and reunites with Rosalina, and in the 120 Star Ending, still has it.
Also, her very first words to Mario in Galaxy 1 are "My name is Rosalina. I
watch over and protect the cosmos."
Now I can't imagine she could watch over the cosmos unless she was all-seeing. That might beg the question as to why the events of the game transpire at all, but as is general god law in most works of fiction, gods aren't supposed to interfere with the affairs of mortals unless mortal threaten the universe and time itself, which is what happened in Galaxy 1.