Yes, but only instantaneously. If at any instant the acceleration were to stop, the speed of light would be $c$ relative to the observer who was accelerating. Acceleration means to continually change inertial frames. In each of those frames the speed of light is $c$ relative to the frame.

Yes, but only instantaneously. If at any instant the acceleration were to stop, the speed of light would be $c$ relative to the observer who was accelerating. Acceleration means to continually change inertial frames. In each of those frames the speed of light is $c$ relative to the frame. Mathematically this may be stated $\frac{dc}{d\tau}=0$.