Guys, here is how you measure latency in a game:
Get a camera that can record 60Hz video.
Hold the controller up in front of the TV and in view of camera.
Hit a button.
Download video to computer.
Play it back frame by frame.
Count how many fields (60Hz frames) it takes before the screen/character starts to react to the button press.
Keep in mind that games often double or triple buffer, so you're immediately looking at 2-3fields of latency just from that. If the game is using vsync then you're doubling that time potentially. Then there is the effect of the way the game is actually programmed (in some cases very badly).
In short, yes, a bad frame rate does increase how long it takes for the game to react to your button presses.