Userscripts.org

Ah, good question!

I'll provide both simple and technical responses:

In no way, shape or form would this script, nor will it ever, violate the user's privacy. It will never track, nor send tracking information; this option simply allows you to customize your own tracking behavior.

[JS decompressed from source-version for explanation]

//Remove Search Tracking 
1 function RST() {
2 	if(uRemoveST) {
3  		lAs=document.getElementsByTagName("a");
4 		for(var iC=0; iC < lAs.length; iC++) {
5 			if (lAs[iC].className=="l") {
6 				lAs[iC].removeAttribute("onmousedown");
7 			}
8 		}
9 	}
10 }

1. 1>2: Run after 1-second delay, If option checked
   
2. 3: Define all page links
   
3. 4>5: Loop through and select links with the "l" classname
   
4. 6: Remove click-event from selected links (thus negating clicked-link tracking)

^As you can see, there is nothing sinister going on with tracking. As stated above, the option [clearly] just lets you turn Google's "remember what was clicked", on or off.

When they construct the search-result links, they include an 'onmousedown' function that fires when your mouse-button literally is in the down position (thus a verified click.)

Since any form submissions or the like ("what the user is searching for") are Sent to their site, yes they can and do track that. If you use your Google login @ http://www.google.com/history you'll notice this. So the difference in the history would be that without that configuration-checkmark, the history would also show (not only what you searched for but) what you actually clicked on.