Well it depends on my xB with the ScanGauge it seems that if the engine is cold or not burning clean yet - maybe from the GP-7 I am using - the MPG on the ScanGauge seems to indicate that gas is injecting with decelleration even at higher RPMs if the engine is cold. When it is warm it is a function of rpm to get the better MPG - going fast enough put it in neutral and increase the coast time but if the engine is hot and you need to slow down then just back off the pedal and keep it in gear. It will not pump much air through the engine but it does pump some and that is not that great for the cat I am sure but you help lubricate the top end of the piston by sucking some oil up there and keep the coolent and oil circulating to cool the hot spots. Flying airplanes the worse thing you can do with a piston engine is to chop the throttle - the engine cools down too quickly and can lock up on you. Less of a problem with water cooled engines however.
As far as the automatic transmission as I said in another thread today DON'T cut the engine with an automatic - it will stop pumping the oil and you will cook the tranny seals and run the gears dry. The oil pump is driven by the engine side of the torque converter and presure is used to engauge the clutches so no oil pressure then no go - no seals no oil pressure and no go - low oil pressure then slipage.
Diesels keep the ignition turned on or else there is no lubrication to the pistons if the engine is still turning over and the injector oil is shut off. On my Geo with the slipping alternator pulley I used to turn off the engine and keep it in gear - this reduces the electric load on the alternator and allowed the belt to catch and the alternator can still keep charging the battery. Pressing on the throttle caused more engine braking than no throttle. My 65 Rambler it was the other way around - letting more air in reduced engine braking. I guess it depends upon the valve timing.