"Connections" are probably more relevant to Nominations than the actual Service Academy admissions. MOC are by nature, political animals, and would likely favor someone that can help them get ahead. That being said, an Air Force 3 star isn't necessarily the person they are looking to please (it usually goes the other way around). With respect to Service Academies, I can't really say connections are that great a benefit, and in some cases can hurt you. USNA does not really look for, or desire , letters of recommendation from other than Math /English teacher, and I would caution against name dropping ...some might not care, some might even be offended. That being said, I'm not naive enough to think that a well placed call from one flag officer to another flag officer wouldn't have some effect.