Linux have one well known feature named as CPU-hotplug https://www.kernel.org/doc/Documentation/cpu-hotplug.txt
In my Intel(R) Xeon(R) CPU, from OS level I can make one cpu core offline.
Technically what happens when I offline one core?
My questions as below:
1) Is that Core turned off (Not consuming power) ?
2) If it is consuming power, is it is consuming power more than C6 state?
The document that you sent is related to how to enable and disable processors in multiple socket boards. It means server boards capable of supporting 2 or more processors (CPUs) and not processor Cores. (CPU Cores).
It is possible to turn off some of the Cores from the BIOS and the power consumption would decrease a little a bit. Cache memory and other features are shared by all the Cores so the active Cores would take advantage of the free memory.