There is no legal way to obtain a moveset with two or more copies of the same move, even temporarily. Mimic and Sketch will both fail if they would have that effect, and you can't use TMs, move tutors, or the move reminder to do it either.
If you somehow did have such a moveset, it behaves strangely. You can click either instance of the move, but it will always count as you trying to use the first one. Once the first one runs out of PP, you can continue to click the second, but it will fail with the stated reason "But there was no PP left for the move!" As such, you can never run completely out of PP, and will never use Struggle no matter how long the battle continues.