Additional contacts of course can have their own email addresses, and the contact name can be the same. The benefit of using contacts is creating multiple billing contacts if multiple people want to receive invoice emails.
What you could do though, if you want people to be able to provide an "alternate email", is to create a custom client field. Settings > Company > Custom Client Fields. Using a custom field for this will allow you to enter it under "Additional Settings" when modifying the clients information, and clients can enter it during checkout, and update it on their own as well.