I think Sawyer's still on the island even in the "we've got to go bacccck, Kaaaate" scene in Season 3, and what Kate meant was Aaron would wonder where she is, as he's probably with the nanny again. In the latest episode however, I think her sneaking off to do something for Sawyer, is connected to Sawyer's daughter Clementine, who he had with Cassidy the woman who tried being a con like him in a flashback in Season 2. He didn't meet his daughter as he was in prison I think, so when Kate left the island he may have asked Kate to find her.
Also something I thought about was how when Claire went missing in this episode, with her (and Jack's Dad), it was a shame Sawyer wasn't awake. He went for a drink with Christian Sheppard in Oz, and a conversation between the 3 of them on the island may have revealed a lot.
Also something I thought about was how when Claire went missing in this episode, with her (and Jack's Dad), it was a shame Sawyer wasn't awake. He went for a drink with Christian Sheppard in Oz, and a conversation between the 3 of them on the island may have revealed a lot.