Some more than others. I think that it can be deceptive though, as bat speed around that area is significantly slower than that of the middle when playing shots, so although the rebound may seem decent, you're highly unlikely going to be able to hit a six from there, unless it's a hook. I do like to test that area though, it never really 'pings' as such, but I've never had a bad bat which has some sort of decent response there, which is why I tend to judge my bats from how well they respond up towards the sticker. (Had a few decent bats with absolutely dead toes)
Paul Aldred's post on FB covers it all, you want the response to be best over the area he has drawn.
Personally I feel that a decent amount of wood up near the top adds stability to the blade overall, but that's just from experience!