So, if Saturn is the "Godhead" of Science and Defense, does that mean he would be the supreme leader of the Marines, like how a Minister of Defense serves as the head of the military in most modern day governmental systems?
Nope.
Top dog within the Marines is the Fleet Admiral
You mentioned chief-of-staff above too, which is a parallel yet separable role entirely that seems to parallel the level of authority of the Admirals and reports to the Fleet Admiral - this officer would be the head of recruitment and likely responsible for running the Fleet Admiral's military drafts etc.
Above said Fleet Admiral is the Commander-In-Chief, who oversees the activities of the Fleet Admiral/Marines and all other WG military forces (e.g. Cipher Pol, unsure if CP-0 is included though) as well as military activity of member nations. Kong is effectively the guy in charge of the Marines as Sakazuki must answer to him, and also the Gorosei above him
Saturn and Warcury will both in different ways have oversight on Kong's activities and role. You'd also expect Saturn to have a lot more input into research and weaponry, while Warcury would be occupying a more strategic role