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It doesn't make much sense, given that it's not receiving light, but looking at that big flat (ish) underside I find myself wondering if it makes sense to add a little shading of some kind or another. Does anyone do this?

I wouldn't waste my time shading the underside. Just paint it and dirty it up a bit and call it a day.

The undersides of models typically get shaded by lights anyway provided it's not mounted high in a display case with lighting coming from all around. The places people tend to want to shade extra are on the side of a model but under something.

Paint the bottom of it with cracks and bright spots of flame peeking through, so when the vehicle explodes you can flip it over for wreckage markers.

I'd just go with base coat and drybrush.

It won't be getting direct light, but it will be getting ambient light. So you won't have dramatic highlights and shadows, but the recesses should still be darker and the open surfaces should be lighter.