Yes, but the warp drive skirts that problem because it doesn’t actually accelerate any matter at all. The matter that is inside the warp bubble remains perfectly still, while the bubble of space itself is what gets accelerated.
It’s analogous to surfing. A wave is moving 40 mph. The actual water is not moving 40 mph, only the wave. But the surfer can ride the wave and be effectively moving at 40 mph, although he appears to be just standing still on top of the moving wave.