You can use a handy function named get_header_image() for this. It will return the image uploaded by a user, or an empty string if a custom header image is not used.
You can base decisions on this query:
if (get_header_image() == '') { // if no header image is present, do this } else { // if we have a header image, do something else }
Note that get_header_image() is not a boolean function, so testing like this won’t work:
if (get_header_image()) { // this is not going to work }
Find more details in the WordPress Codex: