Is is possible using a webform or profile to register for events using only the external id number. Matching the contact via email address (when a user is not logged in) always ends up being messy.
Mike, without a customization you can not do this with events/profile. I am not sure if it can be done using a webform (the webform bypasses the event submission rules)
You can test this, not on your production site, by setting your unsupervised rule to only consider external_ID and see if it works. I'm curious. If that works, then you should be able to use force that webform to use a different rule, but I believe that would also be custom.