Yes, it's possible that they will be gone forever if they have been warned multiple times. However, in most cases, the user will be warned and given a suspended account and limited abilities for disobeying Community Guidelines.
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If you report someone on YouTube, then their comment or channel page will be sent to YouTube staff for review. If the user was found to be violating some form of YouTube's rules like a Community Guideline violation, then action will be taken against the user. Common things include suspensions, or limited access mode.
Under whatever video you are watching there is a flag button. If you click that, the video will be blocked because you thought it was inapropriot.