Uploaded image accessible by many nodes
Yes, any file uploaded into an image field in Drupal is accessible by its File API. 

To address your issue, there are many ways to go about this. One solution that comes to mind is a multistep solution:


Create a content type with an image field. You'll be using this content type to manage any background images you want.
On the node type that you want to add an image background to, add an Entity Reference field that references the node type created in #1 with a Checkboxes/radio button widget.
Edit your theme's template.php to add/update the MYTHEME_preprocess_node($variables) function. Inside of this function you'll be using $variables['node'], node_load(), file_load(), &amp;  drupal_add_css() to retrieve your selected image node reference, load the node, lookup the referenced file, &amp; add inline CSS to your node display.