Do not use invalid email addresses, this will make your account unrecoverable.
If there are other evidences like PGP key or Bitcoin address staked somewhere in the forum, account can be recovered. Email is not the only tool for account recovery but I agree with you that if forum members don't stake PGP key or Bitcoin address, if they don't have an actual email address, they can not recover their account.
Use an email alias instead, like Simple Login or one of Apple's private addresses.
If it is not only about account recovery, use an email like theymos guided (I quoted above).