Is the #disabled form element property different from the html disabled attribute?
Yes it's different, as well as rendering the attribute the form API also ensures server-side validation is taken care of.

As with all Drupal form manipulation, the right way to remove the disabled attribute is with the Ajax API, not by manipulating the input directly with JavaScript.

Once you use that method, you'll be able to get values for the input(s) in the form state as normal.