The answer is "yes", but a falling bullet only has 1/10th of the initial muzzle velocity!
A bullet from a rifle will start at 3,000 feet per second, and stop accelerating when the air resistance balances against the competing gravitational forces.
I a nutshell, a falling bullet travels at about 300 feet per second, or about 200 miles per hour.
I have already addressed the terminal velocity of a cat, (60 MPH) and a skydiver hits terminal velicity at 120 MPH.
Cats hit terminal velocity at 60 MPH
American Army tests from 1920 showed that a 30 caliber bullet hit terminal velocity at about 300 fps, or about 205 miles per hour.
In sum, a falling bullet has only one-tenth of its initial muzzle velocity.
In a vacuum, the increasing force of gravity would continue to accelerate a falling bullet until it asymptotically approached the speed of light. (The “speed of sound” only relates in an environment with air).
In an environment with both air and gravity, a falling bullet will only continue to accelerate until the air resistance equalized with the pull of gravity, an effect knows as “terminal velocity”.
Without air resistance a 30 caliber bullet would start at 3,000 fps and rise to 100,000 feet, taking 90 seconds to achieve peak altitude, and another 90 seconds to fall back to earth.
See my notes on the terminal velocity of a falling bullet.