Must the local PCO termination go through GSA, and if so, how long of a process would this be?

The customer can terminate or cancel any order placed with a schedule contractor. GSA does not get involved in this process. FAR 8.405-4 gives guidance on FSS delinquent performance, 8.405-5 provides guidance on FSS termination for default, and 8.405-6 provides guidance on FSS termination for convenience.