Are having the CPU and motherboard of a computer good analogies?

I am not quite sure what you mean by this, so perhaps a breif description of the two components you listed will help you:

CPU: The CPU (or Central Processing Unit) is often thought of as the Brain of the computer. It is a relatively small chip in standard computers (2 inch square rougly) and serves to compute data. Information from everything else happening in the computer is "fed" to the CPU and it performs data calculations.

Motherboard: The motherboard is like the overseer in a computer. It controls the flow of data, directing traffic. Without this component, all other components of the computer are useless as they cannot communicate with eachother.

Both components are necessities. The CPU its attached directly to the motherboard in almost all cases.