Yes. Everything interacts with everything. Changing Contrast, for example, can change the color saturation and even hue. However, since you are copying settings from another TV, you will not know in which direction the changes may occur. The changes may actually make for more accurate colors. Because of this, I would not be concerned.
WRT the 'crushed blacks': What method are you using to determine black level? If you are using a calibration disk, set the brightness that is correct for your set-up using that disk. Increasing the Brightness level a bit should not have any affect on color accuracy although it may make an improper grayscale at the near black region more obvious. This can be corrected by reducing the visually prominent color using the 10 point white balance menu. Display a grayscale step pattern or a black and white movie with the Color set to zero and reduce the prominent color in the #1 and/or #2 interval(s). Normally, it only takes a one tick down to get rid of the offending tint in the very dark gray areas.