At icloud.com/settings/, under "Apple ID" heading, you can click "Change Apple ID Photo" and upload a .gif as your Apple ID Photo, and it will recognize and display your animated .gif
However, after saving it, it doesn't seem to display the animation anywhere.
Is it therefore impossible to have animated Apple ID Photo?
My way to check would be to do as you have done, but if it isn't working then I am guessing no. It may be something that has to be supported in the software using the image.
IMHO I would find a bunch of moving image to be very distracting.
Click on this link for Apple products feedback links --> Product Feedback - Apple
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Is it possible to have an animated Apple ID Photo?
