I had a ten year old account that was banned for not having an email address. There were various warnings asking me to supply the email address. I refused and the account was deleted. No issues other than this.
Take your E-mail address seriously. After a security incident, Reddit sysadmins may force an E-mail verification and password reset. I lost my first Reddit account (Yes, I lost two Reddit accounts) because of that - the E-mail address was gone since a long time ago but I didn't bother to change that, so I couldn't complete the verification.