At the end of the day it depends on a couple of things - Do you have a real relationship with the dean and is he taking an interest in your application or is it just a standard letter / email he sends to adcom being like hey i know his family/firm and i hope you closely consider him.
I have some friends who were close family-friends with deans/profs at M7 schools and ended up at those schools with decent (not great) stats. similarly with co-workers who have actually worked with deans and profs.
The flip side is I know individuals who were rejected despite a letter from a professor / dean in cases where the letter was sent as an additional letter rather than as a letter of rec. I guess it depends on the individual situation and how much of an interest the dean / prof takes in you. Based on what i have seen with my frnds - its really about how much of an interest the indiv takes in your app. Deans can certainly nudge adcoms one way or another and you can see why - if you have a borderline app will a dean/prof backing push you over comparable students - yes. does this mean you can relax - no because you want to make sure you are atleast borderline which is pretty hard at most of the top schools.