If I make the email field required for both Primary and Secondary Registrants, will I encounter any problems if they both want to use the same address?
Normally there is a site setting that controls how duplicate emails are treated for a TeamRaiser event. This is what prevents a returning user from making a new record every year using the same credentials.
However, as long as the same email is being used for both the primary and secondary registration (and not more than one primary registration), duplicate email addresses will be allowed as long as they are supplied during the initial registration. The child registration will have their own TeamRaiser registration record and their own Constituent360 profile under the parent's email.