Nope. The recoil is about equal to the thrust of a single engine.
Recoil = 45Kn
Thrust = 80Kn
GAU-8 Avenger - The recoil vs. forward thrust myth
A persistent urban legend is that the recoil force of the Avenger matches that of the A-10's engines and as such the plane would slow down, stall and subsequently crash if the gun was to be fired for long periods of time. Some even add the fanciful notion of the plane beginning to fly backwards. These claims hold little truth. While the cannon does slow the aircraft when flying at high speed, it cannot stop the plane in mid-air.
The recoil force can be calculated by multiplying the muzzle velocity with the mass of the projectiles over one second (force = impulse per time). This gives an approximate recoil force of 30 kN. On the GAU-8/A product homepage the recoil force is stated as 10,000 pounds-force, or about 45 kN. The maximum combined output of the A-10 engines is 80 kN. Hence the recoil force of the gun is slightly more than half of the total thrust of the engines. While this is quite significant, it is not sufficient to stop the aircraft.
However, it can slow the aircraft rapidly and poses a challenge for pilots. When the airplane is moving quickly, it experiences a backward force of aerodynamic drag that is proportional to its speed. Aggressive maneuvering increases drag significantly. During combat flight, the engines must operate near full-throttle just to counteract drag and maintain speed. When the gun recoil force is combined with the drag at 400+ knots, the total backwards force is much more than the combined thrust of the engines, even at full throttle, causing the aircraft to slow down. A-10 pilots report that firing the cannon while moving at high speed feels like "hitting the brakes", even though the engines are automatically pushed to full throttle when the gun is activated. Long bursts from the gun can reduce airspeed enough to cause a stall danger when executing a hard pull up and turn at the end of a strafe. Even if the gun could fire forever the plane would never fall out of the sky — it would simply slow down to a speed where the engine thrust is equal to the gun recoil plus the aerodynamic drag.
Some claims have been made that the A-10 engines are susceptible to flame-out when subjected to gunpowder gases, such that when the GAU-8 firing, the smoke from the gun can make the engines stop. Gun exhaust is essentially oxygen-free, and is certainly capable of causing flame-outs of gas turbines. However, the A-10 is designed so that the gun exhaust passes underneath the fuselage, and never ventures near the high-mounted turbines, even during negative-G maneuvers.