it's not mentioned having any effect while he carries Frodo up the mountain, the part where he's tempted is when he's carrying it directly, while Frodo is captured by the orcs in the Tower of Cirith Ungol.

He had feared that he would have barely the strength to lift his master alone, and beyond that he had expected to share in the dreadful dragging weight of the accursed Ring. But it was not so. Whether because Frodo was so worn by his long pains... or because some gift of final strength was given to him, Sam lifted Frodo with no more difficulty than if he was carrying a hobbit-child pig-a-back in some romp on the lawns or hayfields of the Shire.