Can hair particles acquire color from emitter's UV-mapped image? This is a bit convoluted (and I'm still wrapping my head around Blender in general) so bear with me:

I'm trying to create downy feathers on a robin.  I created a basic hair system, cranked up the clumping for a feathery look, made a few weight maps to control distribution and length, and so far so good: fluff achieved.  

But what I'd really like to do at this point is to control the color of the fluff based on where it is on the model.  I have a texture mapped to the mesh already (to cover any bald spots that might show through) but that's not doing me much good since the fluff is covering it.  

Do I have to make a separate system for the red breast?  Or is there an easier way?
Yes you can, In cycles.

In the hair's material, simply add an image texture, and plug it into the color factor as such: