The bullet is being pulled down. That doesn't mean it's dropping.
The acceleration due to gravity is constant, NOT the downward velocity, or "drop".
If the bullet is rising due to the vertical component of velocity, present whenever the barrel is anything but flat, it will not actually be dropping until the vertical component of the velocity vector drops below zero. It will be rising, but ever more slowly.
It is true that gravity begins acting on the bullet, introducing a downward acceleration component to the velocity vector over time, so in that sense, it is dropping as soon as it leaves the barrel. But in a real sense, the bullet sighted in with the sight axis above the barrel, at some distance from the barrel, is not dropping until it reaches the apex of the trajectory.
Acceleration is not the same as velocity.
The upshot is this: a bullet slows over time after leaving the barrel. Gravity's acceleration leads to an exponentially faster downward velocity component over time. That's why eventually a bullet WILL hit the dirt, no matter what. A .22 will hit the dirt at a much closer DISTANCE than a .204 Ruger, which is going a LOT faster and is loaded with a much more aerodynamic bullet, and said dirt-hitting distance is not a linear relationship to the muzzle velocity. HOWEVER, from a flat barrel, the .22 and the .204 will hit the dirt AT THE SAME TIME. The faster round has just gone farther horizontally in that time, since it's going faster horizontally and for no other reason.
The further upshot is that no matter how "flat shooting" a round might be, once it gets out past 400 yards, it'll have dropped a LOT from the line of sight from the barrel. So will any round, because acceleration due to gravity, and deceleration due to wind resistance, catch up to the bullet.