There's a logical fallacy here. That is the assumption that the hierarchy of a military is necessarily based on force. That's incorrect. The most successful militaries rely, in fact, on those at all levels of the organization voluntarily submitting to the instructions of the hierarchy. Militaries are one of the most Darwinian organizational entities out there, at least so long as there is war; unlike many other organizations, they are in fact selected via testing to destruction quite often throughout history.
Anecdotal reporting on the efficacy and survivability of an 'anarchist military' can be found in George Orwell's book "Homage to Catalonia" in which he relates many of his experiences during the Spanish Civil War. Orwell was, at the time, a volunteer in the Republican (Not Communist - thanks Albert Herring!) armed forces - which, if you read the book, seem to operate very similarly to the system gate describes above. Operational objectives are disseminated through the ranks, however the soldiers approach their task with a much 'flatter' attitude to organization. Tactics, organization, logistics, war aims, objectives are all discussed among the various members of this military.
They got slaughtered.
I would venture the opinion that any anarchist group which attempts to operate as a military using these principles will find itself severely outclassed in the arena of high-intensity combat. Time and time again, the value of reaction time or acting time for organizations in combat has shown itself to be a deciding factor, with the organization which is able to act more quickly and with more uniformity of purpose defeating its opponents.
While an anarchist mindset can be said to prevail among various insurgencies throughout historical and present combat, the structure of these insurgencies makes it difficult to apply the term 'military' to them. The definition of 'military' according to our own beloved Webby reads: "Of or pertaining to soldiers, to arms, or to war; belonging to, engaged in, or appropriate to, the affairs of war." To continue the chain, the definition of 'soldier' reads: "One who is engaged in military service as an officer or a private; one who serves in an army; one of an organized body of combatants." Soldier, furthermore, is derived from the Latin soldarius which means 'one having pay.' The word itself comes from the name of Roman coin, the 'solidus', with the implication that a soldier is one who 'receives coin' for his service; who is a paid combatant.
This is distinctly different from combatants who fight purely for conviction outside a formal organization - which is what the above 'anarchist military' sounds like. As such, there is also a semantic flaw in discussing an 'anarchist army.'