Can static objects be enabled/disabled?

If I have a portion of a city that is marked as static, has colliders, and no rigidbody, will enabling/disabling it cause the overhead that moving it would?

I assume you mean the “Static” flag at the top of the Unity Inspector. Enabling “Static” only affects things such as Lighting or built-in Navigation systems. See this link for more info. It does not affect the behaviour of components (eg. Update()).