It's everyone's choice what email to use, but personally I wouldn't use invalid email. As already said above, mostly because of account recovery reasons. If your accouint will get compromised, it will be impossible, or very complicated to recover your account.
If you don't want to use your main email address for Bitcointalk, you can use secondary email for it. Many people have multiple email addresses for multiple reasons.
If I’m confident I will always remember my password, I’d prefer not to provide my email address, because I’ve seen it get leaked in past data breaches.
Good for you. I prefer to use different passwords on different platforms, so, I often struggle to remember it. Like now I don't even know my Bitcointalk password because here I have enabled option to always stay logged in. Also, it's advised to change t change your passwords time from time.