When using / sending a template, is it possible to disable the auto-loading of names and e-mails from the Address Book into the drop-down boxes for identifying the recipients?

You may be able to modify the permission profile for the users to stop the usage of their personal address book (which is automatically populated with every recipient they send to). If you're using the DS Sender permission profile, you won't be able to edit it, so you'll want to create a copy of it and modify the copy - then move your users to that new permission profile. Note: You must be an account administrator to do this

If you update the Address Book setting to be Shared Only, and there are no shared contacts, then they shouldn't get the auto-completion dropdown. If there are already contacts in the shared address book, the only way to remove them is for the user who "owns" the contact to delete it from their address book (by going to My Preferences > Contacts).