No, you do not need your customer code to register for a TWC ID; however, you will have limited access to features that disclose phone service subscription.
Users with limited access will not be able to access:
VoiceZone® to manage voicemails or update home phone settings
Call History to view your outbound call details
Billing to view your monthly statement and go paperless.
Note: you can always provide this information in My Account in the future to gain full access.