A Texture2D simply holds the data of the texture and knows nothing about the way it's going to be rendered. The texture's alpha channel is usually used to create transparency when using alpha blending. If you don't want to create your textures with an alpha channel, you can use the "Color Key Color" property of XNA's texture content processor to create the alpha channel at compile time.

If you absolutely want to define the key color at runtime, you could either use a custom pixel shader that compares the texture's color with your key color and discards the pixel if they are sufficiently similar or use GetData and SetData to create the alpha channel yourself.

I've seen some code snippets with the setdata getdata method of doing this. Will this method be a costly process to do during runtime?

If you only use it once when loading the texture or changing the key color, it's probably going to be fast enough. You should avoid doing it every frame though.