Would arming Earth Spacedock strengthen a Starfleet coup?

One explanation for the original Earth Spacedock's lack of weapons is the Federation Council's fear of a Starfleet coup. A heavily armed station above Earth would give a coup force another powerful asset. The counterargument is that Starfleet already controls the ships and orbital defensive platforms. A further reply distinguishes total firepower from its distribution: concentrating weapons in fewer places could leave fewer loyalist groups able to resist. These are competing readings of the fictional government's defence arrangements.