the only reason to let it set for a while is if you stir then recirculate, you want to reset the grain bed and let it settle for a while to pull all the remaining lose sugar to the bottom and then that creates a filter of sorts
There is never any "loose" sugar in the mash. The sugar is created in solution, and the concentration never gets high enough for any of it to precipitate out. At mash temps, you can dissolve two pounds of maltose in one pound of water, giving an SG somewhere around 1.300. You can't get a mash that concentrated. And, the sugar in solution does not settle in any way.
Nope, not really. When you batch sparge, you want the sugar in solution in the water.
As stated above, all the sugar is always in solution. I believe the point you are trying to make is that to maximize the sparge efficiency, you want the concentration of dissolved sugar to be uniform throughout the mash, rather than have the more concentrated wort primarily in/on the grits. This is the reason for giving the mash a good stir after adding the sparge water (and before the initial run off, also.)
Brew on