No, the writers simply put an erroneous statement in Picard's mouth because they misunderstood "military" to mean "combat-oriented." There are military organizations that aren't focused on combat, like the US Coast Guard, or that are only authorized to use force defensively, like the Japan Self-Defense Force. Starfleet is an armed force with a hierarchical rank structure, uniforms, and courts-martial. It is the primary organization responsible for the security and defense of the Federation. There is no valid way to define that as anything but a military.
Roddenberry was a military veteran and made TOS with that mentality, basing it very much on the US Navy and the British Royal Navy. It was hardly a hedge "from the beginning"; Kirk explicitly called himself a soldier in "Errand of Mercy," and McCoy called him one in "Metamorphosis" (though as a space navy captain, "sailor" might have been more accurate). In "Obsession," Kirk asked Ensign Garrovick for his "military appraisal" of the defensive measures against the cloud creature. In "Whom Gods Destroy," Garth of Izar called Kirk the second-best "military commander" in the galaxy, and though Kirk said he was "primarily an explorer now," that "now" pretty much confirms that he was a warrior in the past.
But by TNG, Roddenberry had come to think of himself as a philosopher of peace and enlightenment, and he wanted to downplay the military elements he himself had built into TOS in the first place. So he portrayed the E-D as a research vessel with a large civilian complement. But he wasn't willing to commit all the way to that change, so he kept the ranks and uniforms and weapons and pretended that being less military somehow constituted being not military.
Granted, references like the one in "Whom Gods Destroy," and McCoy's line in "Metamorphosis" about Kirk being a soldier so often that he sometimes forgets he's also a diplomat, suggest a definition of the word "military" as referring specifically to the combat side of Starfleet's duties. So we're dealing with a case of a word that's used two different ways. Starfleet is unambiguously a military, as a noun -- a hierarchically organized armed force responsible for the defense of its nation. But only some of its responsibilities are "military" as an adjective, in the sense of focused on combat and defense as opposed to science, diplomacy, and other responsibilities. So that suggests a possible reconciliation of Picard's line -- he wasn't saying Starfleet wasn't a military as a noun, but saying its primary focus in the 24th century was not "military" as an adjective in the sense defined above.
