Individual profile schema: No, normally you would not need to collect the ECID as a record as a person could have multiple ECID over time.
Experience Event schema: No, When you enable Profile for an event schema without a primary identity, then the system will remind you to send the identities such as ECID in Identity Map. I going to assume that you will be using one of AEP SDKs: Web SDK or Mobile SDK, therefore the ECID is collected automatically as part of the Identity Map of that event.