All Supes have been grads from the time that there were grads senior enough to hold the position. Obviously, in the early years of USNA (roughly 1845-1865), Supes were not grads. Not as sure about Dants, but don't think there have been any non-grads in recent memory.
Any time there is a change in Supe or Dant, there are some changes at USNA. The mids probably feel it more from the Dant (i.e., liberty, rules). Supes tend to set strategic priorities -- for example, VADM Rempt felt it important that all mids be strong sailors (i.e., sailing vessels) and, as a result, during his tenure, training and academics were tweaked to emphasize this. Cyber has been big for the last two Supes, resulting in mandatory cyber courses and a cyber major.