Yes, I should have phrased it as "no it doesn't help if you go to an Ivy." Sorry.
It has never impressed anyone.
That's unfortunate that it has never helped you because honestly, despite going to a TTT, it helped me land every legal position I've ever had. The first thing the interviewer would say is something to the effect of "well I see you went to Ivy University- that is really really impressive."
I guess this is a situation of YMMV.