To escape an object's gravitational pull you just need to have enough kinetic energy to balance the gravitational potential energy — that is you have to be able to achieve the escape velocity. The acceleration in the article refers to something stationary on the surface of the object accelerating to this escape velocity. As you say the speed of light is constant, it does not accelerate. Therefore if the escape velocity at the surface of a body is greater than the speed of light (so the radius of the body is smaller than the Schwarzschild radius), then nothing, not even light will be able to escape from the gravitational field.
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