Could the rotation vs velocity cancel out the Doppler shifts of light?
Do you mean, could Doppler shift due to rotation cancel out Doppler shift due to radial motion of the object with respect to the observer? Not really, because for a rotating object, different parts of the object are moving at different velocities with respect to the observer: some parts of the object are moving towards the observer, and some parts are moving away. Rotational Doppler shift results in a spreading of spectral lines, whereas translational motion Doppler shift results in a shift of lines. If both kinds of motion are going on, then what you get is broadened, shifted spectral lines.