Assuming there's no email confirmation for linking a battle.net account to a WoW account, yeah.. you totally could.
The login system doesn't really care if the email address registered is valid or not, only that it's unique in the system.
All the same, I'd probably want to get that fixed if I were you, if there's ever an issue that requires them to send you an email, you'd be hosed
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svlyons wrote:
If random outcomes aren't acceptable to you, then don't play with random people.