I think it varies school to school whether they read them or not when they arrive. R2 its probably not as big of a deal since they are just finishing up R1 at a lot of schools so they probably were wrapped up with that until recently or still are.
As for it affecting the difficulty, I dont think so. For a given round I would bet half the people admitted are easy consensus picks, where the committee all agrees right away. The rest are people that they discuss and debate the merits, so if you are an easy admit you still will get in no problem, and the others when you submit will have no bearing on the final outcoming.
Personally I submitted all my apps the day they were due. I think I had one of the earliest admits to Kellogg this year, I found out the last week of November. So personally I think this sort of shows that submitting early isnt going to get you a decision any quicker.