Yes. It doesn't matter what Starfleet considers itself to be in-universe, or honestly even whether Roddenberry and the other people behind Star Trek believe it isn't a military. What's been depicted in canon for Starfleet fits almost every criteria for a military/armed forces by every definition using either a dictionary, international law, or treaty. The Third Geneva Convention defines the laws of war applying to "armies ... militia and volunteer corps" who are: Commanded by a person responsible for their subordinates; Have a fixed distinctive emblem recognizable at a distance; Carry arms openly; and Conduct their operations in accordance with the laws and customs of war Starfleet fits all four of those criteria. They have ranks and hierarchy of command dispensing orders to subordinates. They have distinctive insignia (the Starfleet arrowhead, the UFP emblem, etc.) by which their forces are recognized and organized. Personnel carry phasers openly during away missions, and Starfleet vessels are equipped with weapons openly. And Starfleet abides by the laws and customs of conflict that have been agreed to between interstellar parties (e.g., neutral zones, prohibition of using cloaking devices and biogenic weapons, etc.). In the commentary track for The Wrath of Khan, director Nicholas Meyer at one point talks about that he didn't see Roddenberry's vision for "the perfectability of man" when watching TOS, and there was a difference between what was intended and what was actually realized. Instead, Meyer thought the undercurrent of the show was "gunship diplomacy." The Enterprise shows up at the planet of the week and uses the force at their disposal to cause a change. It's the reason why Star Trek II overall changes the tone of Starfleet to be more militaristic, with David Marcus explicitly calling Starfleet "the military."
But we would see in the Voyager Episodes Unity, and Dark Frontier that Hayes was completely on point. Chakotay was simply exposed to a simple neural link and a the co-operatives neurogenic field had lasting consequences even after said physical neural link was removed, effectively remaining the Co-Operatives puppet. Same with Seven, being exposed to the queen's directed neurogenic signals at the very least brought her back to the Collective. Star Fleet would at least have been aware of neurogenic energy from their experiences studying both Hugh and Picard after they had recovered him, and this proved utterly correct when Picard could detect their presence within FC. It's very likely there's be something akin to a standing order that anyone who wound up exposed and recovered from the Borg be posted to the oppsite direction from them precisely because of the potential neurogenic field possibilities.
Hah! This is Trekbbs. We can, and will, use convoluted reasoning to talk our way out of anything. When we feel like it.
'Kay. Even if all that's true, it still doesn't explain why Picard wasn't removed from the Enterprise and Riker given command for the duration, especially since Riker was the one who defeated the Borg last time. Which was the point I was making.
SF is a military like a fire department is a cat rescue service. Yes, they do it, and they might do it a lot. But it's not their main function, not what they were created for. They simply have the ability, skill, and equipment.
And are the only service to do it for the Federation. So military. They have a different set of laws and members are tried under a court martial, or military court. They can engage in war in behalf of their government. They are not the fire department.
I can see Starfleet as a paradigm shift, like a smartphone. Sure, this mobile computing device I carry can still do cellular telephony but it does so much more— has combined the functions of so many separate devices into one—that to call it a 'phone' is inaccurate, an gross understatement of its abilities. And the way i use my smartphone, being a 'phone' is no longer its primary function, but I can use it as such if I must.
The problem is that a military is a particular legal categorization for a type of government agency with a particular set of legal powers and responsibilities. Starfleet has all of those legal powers and responsibilities. So even if Starfleet's exploratory, scientific, and diplomatic missions are co-equal with its defense missions, it cannot ultimately escape the categorization of military until the Federation establishes a different armed force to defend itself from foreign aggression.