Yes, this is possible. You would continue to use the field named email but rather than set that value to be an email address you would instead pass us a unique ID as the email value.
That ID will show up in place of the email address in your dashboard under the feedback tab to identify each response.
This approach can be used for in-app web and mobile surveys, survey links, and email templates.
Intercom messenger app surveys require an email address, as do email surveys sent by InMoment.