There are two ways to see if a customer has a login. First, in their customer details account, if they have created a login it will say so with a little green flag directly below their name. You can also see the entire list of Customer Logins from your Customers page.
Once a customer has a login account, THEY control their own account, including the email address. If you (as a Punchpass admin) change a customer's email within Punchpass, it does NOT affect their login. The login account is THEIR account and they have control over it.
This is kind of like having a login account to your bank - the bank isn't going to just change your email you use to log in. So changing an email after the fact inside of Punchpass does not change a login information.