Hi!
This should be doable, but with a custom code only. I have constructed a custom filter function, that will execute during the search post-process, and get the ID from the custom field, then get the link to the attachment file based on that id. Just change the $custom_field variable value to the custom field that contains the attachment ID.
Add this custom code to the functions.php in your theme/child theme directory (copy from line 3 only!). Before editing, please make sure to have a full site back-up just in case!
I hope this helps.