Have you ever lautered and then recirculated the wort from the mash previous to sparging? If so, what was the net effect gravity-wise?
I did this yesterday and then I took a gravity reading which turned out to be 1.084. This doesn't seem to be that much different from a straight one time lauter. It may have picked up a few points after running through a second time. Now I wish I had taken a gravity reading before putting it back through as it would have been nice to see how much the already saturated water would pick up on a second run through.
Without starting another 1 part or two part sparge debate I split my 4 gallons of sparge water into two parts and ran it through. I'm not sure what the big hassle is in doing it this way as apart from the pouring and mixing of water with grist (1 minute) it took no longer than doing it in one go.
<-I think I saw this guy in the crowd at the Raiders game.
You probably wouldn't get anything extra, maybe even a little less. What you're describing is more of a very thorough vorlauf than anything, great for filtering the grain particles out, but probably has no effect on gravity.