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: