background_image support multiple image size?

Yes, you can use those images having different sizes.

When you upload an image, by default wordpress creates four images with different sizes like 50 X 50, 150 X 150, 300 X 225 and 500 X 500 and original size of image.So you can use any of them by following code :

    the_post_thumbnail();                  // without parameter -> Thumbnail

    the_post_thumbnail('thumbnail');       // Thumbnail (default 150px x 150px max)
    the_post_thumbnail('medium');          // Medium resolution (default 300px x 300px max)
    the_post_thumbnail('large');           // Large resolution (default 640px x 640px max)
    the_post_thumbnail('full');            // Original image resolution (unmodified)

    the_post_thumbnail( array(100,100) );  // Other resolutions(this will be cropped as per size given by you)

You can use that images in your background but you need to add custom CSS to make it happen as per your desired result.

NOTE: You can always change size of image by going to admin dashboard and then Setting > Media.