Well, it's a complicated answer and depends on whether or not the game uses DX or OpenGL and whether or not your FPS are hitting or capable of surpassing your refresh rate or not.
The primary reason triple buffering is used is so that when the GPU waits for the monitor to reach vertical blanking mode (when it is not updating the screen), it can begin a 2nd frame on the 3rd buffer. With a 2 buffer system, the display buffer can't be changed except between refreshes, and the GPU must hold the finished image and do nothing until it can be flipped to the display buffer. This can result in a huge loss of FPS and adds latency.
With V-sync, triple buffering and OpenGL (not used often these days), when you are able to generate frames faster than your refresh, the GPU will continue to alternate rendering frames on the back two buffers until the display is between refreshes, then it will display which ever frame is the newest in the back two buffers. That means the GPU may throw away rendered frames that never got displayed because a newer one was generated. This method does not add any latency and improves FPS, which improves latency.
With V-sync, triple buffering and DX (much more common these days), when you are generating more FPS than your refresh, the GPU will start rendering on the 2nd back buffer. When both back buffers have complete images, when waiting for a break between refreshes, rather than switching to the buffer with the oldest image to start rendering a new image, the GPU stops, and when vertical retrace mode (time between refreshes) comes around, the GPU will display the oldest complete image. This method results in a full frame worth of latency.
Recap:
With V-sync, when your FPS never reach the refresh rate, triple buffering does not add any latency in either DX or OpenGL and can greatly improve FPS, which improves latency.
In OpenGL with V-sync, triple buffering allows FPS to go beyond your refresh rate, improving latency, and only displaying the most recent images, throwing out extras.
In DX with V-sync, if you reach your refresh rate in FPS, you become limited to your refresh rate, and triple buffering will start to show a frame behind, resulting in a full frame worth of latency.