Yes, ACC works either by releasing pressure on the accelerator (if braking is not required) to match the speed of the vehicle in front of you, or applying hydraulic pressure on the brake system. Of course, when the latter happens, brake lights come on.
Next time you drive with ACC on, roll the windows up shut the sunroof, and turn your A/C and stereo off. Listen for clicking and whining noises behind the gauge cluster. Those are actually solenoids that, similar to ABS, interact with the brake master cylinder to apply the requisite pressure to force clamping on your brake calipers.
Of course, brake lights are an essential component of every braking system. So, it goes without saying that if brake pressure is applied, lights go on.