The connection between her Star Sapphire status and Hal Jordan was actually a retcon introduced by Johns. In the original canon, the Zamarons chose her as their queen because they had a tradition that required all of their rulers to look exactly alike, and Carol just so happened to fit the bill. In fact, the Zamarons actually demanded that she leave Hal behind because he was a man and therefore worthless in their eyes. Carol objected to this and was determined to prove Hal's worth by purposely losing to him in a fight, which in turn led to the Zamarons abandoning her because clearly a woman who could be beaten by a mere man was not worthy of being their queen. Now at this point you might be wondering if there was another Star Sapphire Queen out there who just so happened to be a Carol doppelganger that she would have to battle at some point, and, this being comics, of course there was. This page gives a nice summary: