No, it doesn't. you need to register for chatgpt.

ChatGPT.com no longer requires registration to it ChatGPT-3.5.

go try it right now lol

i assume they still have ip/browser fingerprint based rate limiting, but you can type in a prompt and get an answer with zero login or anything else.

I'm prompted for a login/register. You're likely authenticating via Apple or Google social auth