Note, there's no lighting applied to particles. You'd end up with a glowing thing casting shadow.
Not applied TO the particles, but shadows don't require that. Of course glowing particles done with additive blending wouldn't cast shadows, which is why I specified alpha-blended particles - such as smoke trails, flak puffs etc.
If there's the particle's plane, it can cast a projection. And if the particle's texture has alpha, it should be possible to also project said alpha channel so that it's aligned with the shadow, yes?
If so, then it would be just a matter of computing power to multiply the projected rectangular shadows by the alpha channel, resulting in a shadow that in shape corresponds to the particle's opaque parts. If you want to get fancy you could also convolute the final shadow shape to blur the edges, but that's even further addition to computational requirements.
The biggest problem I see here is that there are ****-tons of particles to be handled so it could pose a huge problem performance-wise. Still, it would be rather righteous to see a fighter spewing dark smoke skim on the surface of a destroyer and have the smoketrail cast a shadow... or to see the bombs or missiles impact a ship with their smoke trails casting shadows to the ship's surface.

But, I'm getting ahead of things, as the system currently only seems to support self-shading. Casting shadows on other objects needs to be done first, and obviously getting things to work for 3D objects is of supreme priority compared to particle shadows.