Consider a Cassandra instance deployed across two data centers for geo-redundancy.
Is it possible configure this cluster with a consistency level such that we get both Geo-redundancy (availablity even if one of the entire data-center takes a downtime and the instance continues to operate with one data center) and full consistent read and write. Does this ask violate the CAP theorem?
No you can't (otherwise you'd violate CAP).
If you want fully consistent read/writes across data centers then you will have to give up availability or partition tolerance.