A "faster" connection (as you're referring to it) doesn't lower latency. A "faster" connection allows more data to be placed on the wire in a given period of time.
Bandwidth is a measure of capacity.
Latency is a measure of delay.
Here's an example of the difference between bandwidth and latency: Imagine 2 internet connections, one 10Mbps and the other 1 Mbps. Both have latency of 50ms. Now imagine that I'm sending keystrokes to a remote terminal on the other end of those connections. For the sake of simplicity lets say that each keystroke consumes 1 Mbps of bandwidth. On the 10Mbps connection I'm able to send the letters A, B, C, D, E, F, G, H, I, J at the same time, so they all arrive at the remote terminal 50ms later and are echoed on the screen... at the same time. Now on the 1Mbps connection each keystroke is sent independently because each keystroke consumes all of the available bandwidth. So the letter A is sent, and then 50ms later it's received by the remote terminal and echoed on the screen, followed by the letter B 50ms after that, then the letter C... all the way to the letter J. It would take 500ms for all ten letters to be received on the remote terminal and to be echoed to the screen. Is the 10Mbps connection faster? No it isn't. It's latency is 50ms just like the 1Mbps connection. It appears faster due to the fact that it has higher throughput (bandwidth) and more data can be placed on the wire at one time. That's the difference between bandwidth (capacity) and latency (delay). In the strict sense, a "faster" connection (in the way you're referring to it) will not reduce latency.