Saving memory when creating textures

When the space between UV islands is filled with black color(the texture file is being masked) the saved PNG file takes less space then when it is not. On the other hand BMP format takes the same space on disk in both cases. I guess it is because of the lack of compression. I understand that textures in unreal are later being converted to DTX formats. So I have a question: do converted textures take less space on a graphic card if masked with black color or not?