Most the time it'd make them go boom
Only if all the engine criticals in the same section were destroyed, and even then that only gave a small chance [IIRC about 3%] of an actual engine explosion. [Usually called a stackpole.] There's a variant rule about taking 4 engine hits in one turn that increases your chance of exploding, but it's generally not used and relatively superflous as if you can take 4 engine hits, you're probably going to die soon anyways.
The lack of engine criticals in the left and right torso is what gave some mechs, like the Warhammer IIC extreme survivability. Typically a mech would be dead once a torso was destroyed since a third of the engine is going with it, but mechs like the Warhammer IIC have smaller engines that fit entirely within the center torso, and as such, only destruction of the head or the center torso would put one down for good.