No, he didn't. And the reason he succeeded is part of what makes it so wonderful. Frodo refused to kill Gollum because he took pity on him because of the Ring. It was Frodo's refusal to kill Gollum that let Gollum play the ultimate role at the end. Had Frodo listened to Sam, and either banished or killed Gollum, the Quest would have failed. Frodo's kindness saved the quest.
Still, Sam's always been my favorite anyway because he did the single most courageous act in the book when he picked up the Ring from a "dead" Frodo and continued on by himself. He gave up the thing he cared about most in order to do what what right.