Modern cars do shut off the fuel when coasting with no throttle!
The manufactures got this sorted ages ago trying to reduce offical MPG figures!. So shifting to neutral won't help (except at v low speeds).
I'm not sure if MBs do this, but bAd124 and I both have Audi's with trip computers. If in neutral while coasting, the computer reads '200 mpg' - it's maximum value, but signifying it's still using fuel. Now if you stay in gear and coast it switches to '- - - mpg', and you're now not using any fuel. In an automatic this may only occur when in 'lock-up'.
Also, in a modern(ish) diesel, if coasting in gear, its nearly silent, because no fuel is injected and there's no combustion. Then even the slightest throttle opening introduces the 'clatter' as the injectors inject fuel and combustion occurs.
2.5-16v 1990 90,000m Astral Silver
2.0E 8v 1986 107,000m Black