Not exactly.
First, each Cb and Cr (could also be UV) channel represent the deviation from gray on an axis ( from wikipedia : CB/PB and CR/PR are deviations from grey on blue–yellow and red–cyan axes, whereas U and V are blue–luminance and red–luminance differences.) (The LAB colorspace is using the same principle)
So for example, the CB/PB channel representation in 8bit is at 0 - blue full saturated, 64 - blue half saturated, 128 - grey, 256 - yellow full saturated.
Second, in the 4-2-2 relationship, the 2-2 doesn't not represent the channels, but samples per row. The sampling formula always seems to be represented on by 4 pixel columns by 2 row. So in a 4-2-2 sampling, for a region of 4 pixel wide (4-x-x) by 2 (the second row - not related to the 2s in 4-2-2), you have on the first row, 2 samples of chroma (for both U and V, or Cb and Cr), and on the second row, 2 samples.
So, on a 4-2-0, on first row, 2 chroma samples of each channels, but no sampling on the second row (it is like have half resolution on both x and y axis of chroma versus luma, eg. 1920x1080 luma resolution, 960, 540 chroma resolution).
In 4-1-1, you have one sampling of chroma on each row (so for a 1920x1080 luma resolution, you get a chroma resolution of 480x1080).
in 3-1-1 sampling, like XDCAM EX and HDCam HD, you have for each 4 pixels of luma in source, only 3 samples of luma at the output, that is why those codec are 1440x1080 with a 1.33 pixel aspect ratio.