No. You can analyze a swing in Motion Lab without one and see the summary, the visual proof and the main issue. A free account unlocks your One Fix, practice plan, retest and progress.
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Without an account, everything you do is kept in this browser on this device. A finished analysis stays there and carries over when you sign up or sign in, so you do not have to film it again.
The account exists because a fix is only useful if it is still there when you practise and retest. It also lets your progress follow you to another phone or computer — see syncing across devices.