Theoretically, mixing pigments with a carrier of some sort, you are just making paint, as that is what paint is made from are pigments.

That being said, you need a very small amount of pigment to mix with a carrier, and the likelyhood of getting the pigment mixed properly with the carrier so it doesn't settle out in your airbrush is probably going to be next to impossible. The pigments used in model paint are alot finer than what you can buy in a pot of weathering pigment, as well weathering pigment has a binding agent in it so it will stick to your kit, pigment in paint wouldn't and I think the binding agent would make it much harder to get the pigment mixed with a carrier so it wouldn't clog your airbrush.

Further more, a .25mm needle/nozzle, way too fine to be spraying that type of concoction, I would think you would need at least a .4mm or larger needle/nozzle set up.

Mix up some pigment with your favorite thinner, get an old brush into the mix and load it up, put the brush between your kit and your airbrush, and spray just air from the airbrush through the paint brush loaded with the wet pigment mix, and blow the pigments onto the kit to create mud splatters.