Is it possible to animate Ambient Occlusion in Cycle renderer?

I am rendering an animation which has a HDRI sky with changing ambient occlusion distance / fading factor by using keyframe and Cycle rendering engine. Blender version is 2.93 Beta.

If “Persistent Data” was set to ON, it was found that Blender will not make change to the Ambient Occlusion Distance value, unless it is set to OFF.

It was noticed that in Blender, some keyframable items have the “Animate Property” attached (eg. transformation) and some have not (e.g. Ambient Occlusion). Does it mean that Ambient Occlusion is not animatable?

Also in Blender 3.0.0 Cycle-X branch, Ambient occlusion seems does not work.