Unfortunately that flag only sets military support costs, not support costs per unit. You still pay 1 gold per unit per round, including for workers. Military units have additional costs depending on what civics you have and whether they are in your own territory or not. Some civics like pacifism can add more costs, and then you pay extra if you're not in your own territory (for military units). But anyway there is still a support cost for a unit whether that flag is checked or not.