When using the AlphaTest technique with just a Diffuse texture, everything works fine. However, if I add a Normal texture, then the AlphaTest technique stops working. The transparent parts of the Diffuse texture are drawn as a solid white color. Is it possible to have the AlphaTest technique test against the alpha channel of the Diffuse texture only, regardless of the other textures added to the material?

you should add textures using MeshEditor/WorldEditor Material Editor.
if normal map is used, alpha is stored in the secondary GFX.

Yes, I am using the Material Editor in the Mesh Editor.

I drop a Diffuse texture on to the Diffuse slot. I can then slide the Color Alpha slider up/down to adjust the degree of alpha testing. This works well.

However I then have a second normal/specular texture. When I drop this on the Normal slot, the Color Alpha slider stops working. Sliding it up/down has no effect and the transparent parts of the Diffuse texture are drawn as solid white.

I can take some screen shots to show you if you like.

You should drag and drop all textures (diffuse, normal, specular etc) at the same time on Mesh Editor window.