I've never encountered a gearbox that coasts - if by that you mean it goes into neutral with the engine idling (*). That probably uses more fuel than leaving it engaged with the wheels: an idling engine needs a token amount of fuel to keep it revolving at idling speed, whereas an engine that it on over-run (wheels keeping the engine turning) can shut off the fuel completely.
I've seen this with the instantaneous fuel consumption gauge on my car's trip computer. Press the clutch while going down a gentle hill and the consumption decreases to about 200 mpg while the engine is idling, but release the clutch so the wheels keep the engine turning and the consumption decreases still further to a nominal 999 mpg as the ECU cuts off the fuel altogether. Of course, set against that is the fact that the car won't travel as far before you need to put your foot back on the power once the hill has levelled out, because of the very slight engine braking even in top gear. And the amount of fuel saved will be pretty minimal, I'm sure.
(*) I realise that coasting or free-wheeling is standard on crankcase-scavenged two-stroke engines, because a fast-revving engine with no fuel going into it means the bearings will not be getting much lubrication. I presume that two-stroke cars have heavier-duty brakes to counter the fact that you cannot use engine braking on a steep hill and must rely entirely on disc/drum brakes.