Can I access a mesh's local vertex positions in Cycles Nodes? I'm looking to use a mesh's local vertex data (absolute distance from 0 or origin) for the FAC on a color ramp thus allowing me to grade the color based on distance from the Origin. Is there a way to get this data from a node in cycles? 

This is to make a coal with an Emissive Color ramp that will have a Dark black\red for the tips of the coal and a brighter warmer orange/red for the bits closer to the heat.
You can easily use use the Object texture coordinates from the Texture Coordinates node to achieve this.

The socket will output XYZ values in object space, than can be used as RGB values or mapped with a Color Ramp node.

All you have to do is use a Separate XYZ node to get the Z component of the coordinates, and optionally a Math node set to Absolute so you can easily have symmetry along Z, if that is what you wish to achieve.

 

Taking this a step further, you can calculate the distance as sqrt(x^2 + y^2 + z^2) (and remove the Absolute node) as follows :



Feed this into a 'Multiply' Math node to allow you to scale it as necessary and link this into the Color Ramp.