Yes, create/edit permission will allow them to edit pages after creation.
There are some add-ons that enable more form-like entry, which can (optionally) stop a user editing a form they filled in after entry, but the problem here is that if they're anonymous, Confluence has no way of knowing who they are and hence which copy of the form they entered. Your first user would enter a form and no other anonymous users would be able to.
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