Do video formats support colour profiles?
No most video formats (nearly all) do not allow custom ICC color profiles to be embedded. (Improvemet/correction: MP4s can have color profiles tagged in the metadata of a video file.) most video on the consumer end is intended for the REC.709 color space. sRGB is similar and uses the same primaries. transcoding (including compressing) will almost always result is a slight shift in color accuracy, saturation, gamma curve, or black and white level shift. This is made worse due to converting between RGB and YCbCr color spaces.