Well, it's possible to set an additional color for an object (using Object3D.setAdditionalColor(java.awt.Color col)). But lighting is multiplicative when using the OpenGL/SoftGL-renderer and so the object will look like fully illuminated even if it isn't...but it won't look white.
The only way to achieve this, is to replace the texture for the object with a white one (but that's rather slow and works only if the object has one texture only (like an MD2-model or similar)) or by replacing the texture of the object in the TextureManager using TextureManager.replaceTexture(...). Problem with this is, that you'll replace the texture for all objects using this texture. It could be possible to do something like this:
// init
Texture t=new Texture(...);
texMan.addTexture("tex1", t);
texMan.addTexture("tex2", t);
texMan.addTexture("tex3", t);
obj1.setTexture("tex1");
obj1.setTexture("tex2");
obj1.setTexture("tex3");
// replace
texMan.replaceTexture("tex1", whiteTexture);
texMan.replaceTexture("tex2", redTexture);
texMan.replaceTexture("tex3", blueTexture);
...
// replace again
texMan.replaceTexture("tex1", t);
texMan.replaceTexture("tex2", t);
texMan.replaceTexture("tex3", t);
But i never tried to add the same texture multiple times to the Manager that way...it should work, but i'm not sure.
Hope this helps.