Changed the battery on my Mk II and the fuel economy is pretty rubbish, just below 8L/100km, is the IDLE relearn thing needed for the MkII or is it an old wives tale?
Never relearned an ECU on any car, and changed plenty of batteries,,, All the base parameters required by engine are stored in non-volatile memory safely inside the ECU, modern ECU are capable of adjusting parameters to suit your driving style and this is stored in volatile memory probably backed up by a capacitor to deal with short power losses, and after battery change they will relearn , but the base parameters were there when car was new and are still there now. I always prepare everything by taking off battery clamp and moving anything out of the way - slackening off battery terminals ready for the quickest possible changeover, but last few time I have used a home-made cigarette lighter power lead with 20 metres of twin speaker cable and two cigarette lighter plugs - you need a second vehicle or 12 volt battery ( watch the polarity - centre prong is +, which is where the stripe on speaker wires comes in ). Turn ignition to first position on both vehicles to connect cigarette lighter power main car power and you can take all day to change battery if you like.
you can use one cigarette lighter plug and a spare battery to do same job, just need a pair of red and black crocodile clips on other end of the lead.
EDIT - Have attached photo of home made battery change kit - to be honest it does not need to be heavy duty speaker cable as shown, as it is only carrying a few amps ( unless you have heated screens, mirrors, headlights etc turned on in car you are changing battery on... I turn everything off to reduce current required from donor car.