Define the alpha on a GUI material component (in editor)

I'm not sure exactly what you mean by "background" alpha, but if you're talking about the transparency of an object with that material, then this totally depends on the shader you're using to render that material. Many shaders either don't use the alpha value, or use it for something else than you expect. Keep in mind that there's a reason alpha is called alpha, and not just "opacity" or "transparency". :) Those last 8 bits of a standard 32 bit RGBA value can be used to store any kind of information to go along with the RGB value, depth for example.

If you want to define the transparency of an object in the editor, you have to render the object with a material with a shader that uses the alpha channel for transparency. Examples of these are the particle shaders, or all shaders in the "Transparent" subgroup, except for "Cutout".