Lag is cumulative: any and all lag will make a difference. What’s more, in a BYOC tournament (as is typical) stick lag is one of the easiest things for a player to manage. Tests like Toodles’ recent video demonstrate that stick lag does in fact make a difference within the game.
You could claim that a difference 0.003 seconds of lag is too small an advantage to care about when player reactions are going to be 50 to 100 times as long, and variability in reaction times is apparantly on the order of 10-20 times that. (http://en.wikipedia.org/wiki/Mental_chronometry). Though, as they say, absence of evidence is not evidence of absence - things can easily make a difference without players noticing.
However, it’s pretty clear that players don’t bother to care that much about reaction times on that scale. For example, reactions to audio cues are about .030 s faster (yes, that’s two full frames) than reactions to visible ones, but we don’t see people talking about how to use that. (In fact, Daigo famously wears sound stoppers - not head phones.) Similarly, it’s a little less clear with the new generation of displays, but NTSC CRTs update the top of the screen first, and I don’t see people suggesting looking at the health bar as a technique for improving hit confirm rates.