Is it's possible to update WordPress incrementally to the latest version if it's been a wile since WordPress was updated on my site?

Yes you can do this via a manual update. 

  1. Take a back up of your site.
  2. Download the WordPress version you need from the WordPress website.
  3. Using your file manager program navigate to your website root folder. Delete the old WordPress folders  ‘wp-includes’ and ‘wp-admin’.
  4. Replace them with folders from the new installation. 
  5. Overwrite any files in the wp_content directory with the new files.
  6. Copy the root directory files from the new version in to the root directory of your existing website.
  7. That’s it. Test your site to see if it works.