The original question refering to Cost Index altering due to engine out.
I could not find anything specific to that Question. However our company FOM states that you must have an ALt. Airport within 60 minutes at the one engine inop. cruise speed. (approx. within 340nm, A320)
Refer. to the QRH IN-Flight Perf section, EO. long range cruise. This gives target N1,Mach, FF, IAS. for given FL,WT,ISA.....
Also the company SOP states. Econ cruise (normal ops) is a variable speed dependent upon the cost index chosen for the flight.
My guess: in order to meet the QRH specs. to be as acurate as posible this would be have to be flown in selected SPEED/MACH.
Under extreme conditions (ie very strong head or tailwind conditions) the Bus will change its speed/Mach to what it calculates for the given cost index for the flight conditions.
(wind and all the other variables. I am not sure if this is the same for Engine Out though)
When an engine is failed, you will get an EO clear prompt. if this is not cleared; fuel predictions for EO are available on the appropriate page. So if its critical, I would look there first then the QRH and fly selected SPEED/MACH. Therefore you know what your getting..
Hope that made some sence..
Rob