Roy Childs argued persuasively that it does, in his famous 1969 open letter to Ayn Rand.
The state is that institution (or hierarchy of institutions) maintaining in a geographic region a formal monopoly on the authority to use 1) retaliatory force and 2) force initiation (to whatever extent it is allowed). I indeed can (barely) envision a minimal state financed entirely without obvious ongoing coercion — e.g., interest on an endowment, collection of land rents, fees and auctions for natural resource use, and fines (perhaps collected like taxes) for pollution. What I can't envision is how a state would maintain its monopoly on retaliatory force in the presence of vigilantes who insisted on their ZAPsolutist right to conduct their own retaliations without any oversight. If an institution oversees the retaliatory force only of the people who formally sign up, then it doesn't have a monopoly and so it's not a state, but rather is more like a neighborhood watch club on steroids. Thus ZAPsolutism will always either reduce to anarchism or allow for exceptions that make it morally equivalent to coercive minarchism.
Some proponents of zero-aggression minarchism deny that essential services like national defense would be have to financed through what is in effect an anarchism-style passing around of a collection plate. They argue that some of the fees that government charges for services only it can provide could be used to finance services (like national defense) that would be under-funded due to free riders. This plainly advocates that government exploit its monopoly on certain services to deliberately over-charge users of those services in order to provide benefits for other people. This is morally equivalent to coercive taxation. The problem of deciding who and how much to over-charge for an essential service is no different in principle from the problem of deciding who and how much to tax for national defense.
Some minarchists indeed claim absolute fealty to the ZAP while advocating a state monopoly on law enforcement, but their position seems to be either incoherent or functionally identical to deontological anarcholibertarianism. If a lifelong coercion abstainer nevertheless refused to recognize the state monopoly on law enforcement, then either the state would have to coerce him or the state would have to surrender its monopoly and would be just another voluntary anarcholibertarian protection agency. If an institution has no more authority over you than what you've voluntarily granted it by explicit contract, or if you can decline to recognize its authority or opt out of its authority without emigrating, then that institution is a club or maybe a standards body, but not a state. And if the state is going to violate ZAP and coerce a lifelong coercion abstainer for the goal of uniform law enforcement, then that is morally comparable to the minarchist state of Milton Friedman and Mises and Hayek that violates ZAP to collect minimal taxes to finance universal law enforcement.
If an institution can qualify as a "government" but have no more force-initiating power than an opt-in club, then merely saying you favor "limited" or "non-coercive" government does not distinguish you from an anarchist. Anarchists don't oppose opt-in clubs either. If you eliminate the government's monopoly on coercion, you eliminate government, and what you have left is more like AAA or a book club.