Automatically make an uploaded file available for download

The only way you could do this is if the form is creating a post. Then you would use a Post Custom Field and set it to be a File Upload field. The file uploaded (in this case a PDF) would be uploaded and the full path to the file would be stored as the value of the custom field. You could then display this custom field PDF link by editing your theme template file or using the Post Content Template functionality to insert it automatically into the post body.