Only the defined color of the model will show in the capped part of the cross section, not the applied texture map.
If it is critical, you can try a temporary extrude cut and this will show the texture map because it is now a true part surface.
I have to do this in many of my assemblies where I needed shaded sections in drawings. I create a next level assembly and use an extrude cut on the entire assembly model. I can then change each cut surface to a "sectioned color" I want much like the show-n-tell models machinist love to make out of transmissions and such.