Top-fueldragsters don't even have sparkplugs, neither do RC-nitro engines. And yes, it works through the same principal as a diesel engine. Self-combustion by compression.
And yes, the dragsters stop their engines by cutting the fuel. Something which is pretty hard to do on an engine with a float-bowl carb. You could cut off air completely, but I don't know what effect that would have.
This is why I'm not touching nitromethane: