They would have adapted.

The Borg would have simply developed shields to deflect the bullets. Just as the main shields deflect small particles and debris, the borg would have fashioned similar shields to stop the bullets.

adapt

Well, first off, The Academy does train ensigns in hand-to-hand combat, but no human crewmembers carry knives and swords. The klingons carry their weapons because its almost part of their religion. For the second part, the borg would adapt to the machine guns after a couple shots and you would have 20 or so useless machine guns lying around.

No Replicating Weapons

All Replicators onboard Starships cannot replicate any form of weapon. It's a safety feature that Starfleet had put on all of the replicators. Now when Picard is on the Holodeck shooting the Borg he is using a Holographic gun which would only be able to be used on the Holodeck. Like Voyager's Doctor. He can't leave Sickbay unless he has his mobile emitter because there aren't holographic projectors on every deck.

Adaptation

Picard only killed two Borg with his Thompson. The inference is that eventually the Borg Shields would adapt to stop bullets.

In that case

If the borg would adapt to bullets, then by the same logic, they should adapt to knives and other hand weapons. poor klingons....

original nitpick is right

The Borgs cannot "adapt" to attacks that carry kinetic energy. They cannot adapt to a knife, a sword, or a bullet. Star Trek takes some things a little far scientifically, but that would just be too much. The Borg adapt to electromagnetic attacks only. They cannot adapt to a projectile weapon. Starfleet should have used those weapons to defeat the Borg. The Borg do not deploy a shield like federation ships do, they alter their frequency resonations to deflect electromagnetic attacks. That is why in the Best of Both Worlds Worf and Data were able to pilot a shuttle through the borg shields, because a shuttle is solid mass with kinetic energy. If they had tried to pilot the shuttle through the enterprise shields the shuttle would have been destroyed. The reason that the borg do not have reasonable defenses against projectile attacks is because any race they would be interested in assimilating would not use projectile weapons. Projectile weapons are expensive, bulky, and there is a limited supply of them on board any ship. No advanced spacefaring race would use them.

Borg Shileds Only Adapt to Energy

Borg shields only adapt to energy weapons. Aside from that, safety locks can be broken. I know in a DS9 novel (Fallen Heros) they were able to replicate phasers (but not their energy since you can't replicate pure energy). So, given time, I'm sure they could disable the safety locks.

Holodeck machine gun -is- an energy weapon

It wasn't actually bullets hitting the Borg, but tiny holographic images of bullets, given substance by -force fields- a form of energy. So, any argument that the Borg shields can only adapt to energy based on the holodeck machine gun is moot.

on 41204

No, it was not holographic images of bullets. The holodecks work by using transporter/replicator technology. Those were real replicated bullets. We know this because Picard "disengaged the safety protocols". Even if they were just holograms surrounded by force fields, a moving force field would still have kinetic energy. In addition to all of this, the argument that the Borg only adapt to electromagnetic attacks is not based just on this scene. In the Best of Both Worlds, Worf and Data piloted a shuttlecraft right through the Borg shields, but anything the Enterrpise shot at the Borg ship was ineffective. The enterprise attacks did not have kinetic energy. The shuttlecraft did. To say that the Borg can adapt to projectile attacks is silly. That would mean you could fire a missile at a borg and it would just bounce off. Impossible.

"We shoulda brought shotguns"

The subject line is actually a quotation from "Pulp Fiction" rather than "Star Trek: First Contact," but it reflects my agreement with the original nitpick. I kind of understand how the Borg could adapt to one frequency of an energy weapon before adapting to another, but not how such incremental adaptation would work with solid weapons. For example, if one were to fire .357 caliber bullets at a bunch of Borg drones, would they develop shields to deflect bullets of that size but still be vulnerable to, say, .38 caliber bullets? Similarly, if you stabbed a couple of Borg with a knife with a 5-inch blade, would they block out such blades in the future but not, say, 7-inch blades? Would they adapt to bullets or knives of all sizes simultaneously? How would their individual "defense systems" (for lack of a better term) distinguish between weapon sizes? For example, would it "say," "We're immune to .357 bullets, but this is a .38 caliber one, so we'll let this one through"? If they confronted a race whose members were physically strong enough to damage the Borg with their bare hands (which obviously humans and Klingons can't do, but Data can), could they adapt to one person's right fist but not to his/her left fist or feet or another person's fists? If, in the deflector dish battle, the Enterprise officers had reused Picard's tactic of shooting a hole in the hull of the ship so that the air rushing out would blow a Borg drone into the space, would the Borg have been able to adapt to that? Would it have made a difference how big the subsequent holes were? Because, as illustrated above, the issue of adaptation to solid weapons is so murky, I think the writers avoided having the Enterprise crew use the same type of solid weapon repeatedly against the Borg so that they wouldn't have to deal with the issue at all.

Adaptation to photon torpedoes?

The above discussion, of the Borg being unable to adapt to weapons utilizing kinetic energy, is a good explanation for why their shield did not prevent the Enterprise's crew members from beaming onto the ship in "The Best of Both Worlds, Part II" to capture Locutus. But don't photon torpedoes have kinetic energy? I assume that photon torpedoes in the "Next Generation" time are solid, as they were in "Star Trek VI" when physical torpedoes were loaded into torpedo bays and the crew was able to plant gas-detecting equipment inside one such torpedo so that it could find the cloaked Bird of Prey. Flying through space, these solid torpedoes have kinetic energy. Yet even back in "Q Who," Starfleet's first encounter with the Borg, the photon torpedoes were completely ineffective from the beginning -- the Borg adapted without first absorbing any opening shots -- even as the Enterprise was able to damage the Borg ship with its phasers. Later, in "The Best of Both Worlds," it appeared that only the phasers worked against the Borg ship, when they were used to knock out a tractor beam.