Can you use another material as input to material nodes in cycles? Is it possible in cycles to use setup a material node to take the output from another material as input into a mix shader?  This way if I change the configuration in the other material it updates both materials?  Or do I need to do this another way?

I'm surprised nobody has asked this already and can't find anything online so maybe it's not possible.
That's a typical use case for Node Groups. 

Select all relevant nodes and group them with Ctrl+G. This way the created group is accessible within all material node trees, located in the Add menu: Shift+A > Groups > Your Group Name.