It depends on how you plan on using the email address collected for the user. The ATT guidelines require ATT permission for "tracking", and:
Tracking refers to the act of linking user or device data collected from your app with user or device data collected from other companies’ apps, websites, or offline properties for targeted advertising or advertising measurement purposes. Tracking also refers to sharing user or device data with data brokers.
So if you are using the email address just to send them email or keep track of their data internally, that seems fine, but if you are linking the email with data collected from other companies then you need ATT approval.
If you are planning on uploading email addresses to Facebook or other ad companies for lookalikes or retargeting purposes, or basically giving the email address to any company outside your system, then you are in ATT territory.
Hope this helps!