If he is going to be here for the long haul, which is what it looks like from what I can see, then I believe that yes, he has more say in how things are constructed than previous coaches.
If they really do see him as a potential Zidane/Pep/Klopp type of guy, then they need to concede a little of that control. Let's be honest. IF the CL is their ultimate goal, then their current plan for the last 9 years of not giving the coach any say, has failed on numerous levels. It doesn't mean they can't change their way of thinking. Agnelli is certainly young enough to be able to adapt.