No, you don't have to send us the end-user created_at date in order to run Wootric.

But we certainly recommend doing so!

Why?

The created_at date helps the system identify when a user becomes eligible to see a survey for the first time. Our default is to identify a user as eligible 30 days after their created_at date says they were created in your system. We do this because we only want you to survey users that have actually used your system and can give you higher value feedback. We also don't want to survey someone who doesn't have a (well-formulated) opinion thus unfairly surveying them and (incorrectly or adversely) affecting your score.

If you decide not to pass us the created_at date for your users, we will consider them newly created in your system. This means the clock starts ticking from the moment the user logs-in and the Wootric SDK creates a cookie for them. They will become eligible to see a survey after the throttle days have passed that you have set in the Wootric settings.
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FAQ: How does created_at date get used when it comes to sampling my users?
See this other Customize Sampling help article here.