That's one of the main reasons for the dark frame as normal chroma and luminance noise really can't be removed with a dark frame as I understand it.
Indeed, employing a dark frame actually makes chroma and luminance noise
worse. At every pixel where a dark value is subtracted, you are adding a second readout noise component. This type of noise adds in quadrature, thus 2 frames (original and dark) leads to sqrt(2) = 1.4x the readout noise of the original frame alone. You are also left with the residual shot noise of the dark currents, as the dark frame can only subtract an estimate of the dark noise. That can be even worse than the combined readout noise.
Of course, there's no doubt that being left with lots of random noise is still far better than leaving the image with tonnes of uncorrected systematic dark current.
Bottom line is, a clean image not requiring a dark frame is always best of all!
Ray