Short answer, no. But here's some suggestions (in order from easiest to hardest) that might be useful to meet your end-goal of learning about the colour space.
The eyedroppers link mentioned by @Stan has many apps that provide variously RGB, CMYK, HSV/HSB, HSL and conversions to various standard representations of those (e.g. for HTML). While that doesn't fulfil your need, you could contact several of the developers of these applications and suggest they add support for YCbCr. It'd be fairly straight-forward in many cases, if they are still actively working on the app and see it as a possibly useful feature (especially if you mention that there is no other YCbCr colour picker in existence).
If you just want to explore the colour space, you could have a look at this YCbCr colour picker (or this one) and see if that helps you sufficiently. It's not choosing from an image directly, but it does let you see various mappings between RGB and YCbCr (and indicates when you go outside the RGB gamut).
If you have a bit of patience, you could use this online colour converter to convert directly from RGB values to (amongst others) YCbCr. But you'd be doing that one-colour-at-a-time.
If you happen to have access to Matlab (and know a little about how to use it), you could use the rgb2ycbcr function in the image processing toolbox to convert your images in entirety to YCbCr. From there it'd be a fairly simple matter of plotting the image, using
ginput() to let you click on it, and printing out the YCbCr values from the image at the clicked coordinate.
Finally, if your maths & programming skills are up to some simple scripting (even if not a full GUI application) you could use the conversion algorithms to easily convert from, say, HTML hex values copied from one colour picker, into YCbCr values from