When a user under 13 creates an account, does Neopets store the user's email address?

No, we do not store email addresses of under 13 accounts in a retrievable form in our system.
After sending a one-time email containing an activation code, we "hash" the email address, a process in which it is translated into a long string of letters and numbers that doesn't identify the user and can only be used by the user to, for example, ensure that the account limit is not exceeded.