How does the addition of Chicory affect coffee?
Roasted chicory root (which is what you are adding to coffee) contains no caffeine.  

What chicory does is add a nice, roasted flavor to coffee, which is desireable either for cultural reasons, or to offset the bitter flavor of over-roasted low-grade coffee beans.  Originally, it was also added because it was much, much cheaper than coffee.  That's not true anymore, even in India as far as I know.

Proper New Orleans or Vietnamese coffee also contains a lot of chicory.