Does it affect flight. Of course, but not to the point that you will ever notice it in the scenario that you offered.
Without getting too wordy, your projectile is moving along the x-axis at approximately 1000 mph (about 1500 fps) and that, coupled with the weight of the projectile, gives it quite a bit of momentum (inertia). Gravity acts upon the projectile along the negative y-axis at 32 fps/per second whether you drop the bullet or launch it at the aforementioned velocity (that is why a bullet dropped at the muzzle will impact the ground at the same time as one fired, regardless of initial velocity . . . the initial velocity just determines how far from the muzzle the fired projectile will land).
I digress, the point is that the momentum in the negative y direction that would be imparted by rain drops weighing next to nothing compared to a bullet and traveling slowly (far less than terminal velocity because of atmospheric resitance) compared to the velocity along the x-axis would be neglible, but of course existant.
That said, you might be able to tell the difference at the range you quoted if your rifle was capable of one hole grouping, but in a real world analysis . . . take the shot my friend and enjoy the venison!