I don't know about the length of startup, but it is true they are left on 24/7. Tales from third shift custodial almost always include how creepy it is to work an attraction with the AAs moving and no soundtrack.
There are many repurposed AAs around. A partial list might include:
Splash Mountain: most of the AAs came from America Sings.
Star Tours: a couple of the robots in the queue are geese from America Sings. Look for the robots with the webbed feet.
Some Pirates AAs came from World of Motion, and Mother from Carousel of Progress apparently makes a background appearance in Mission:Space.
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I believe the AA are left on all night but I'm not 100% sure.
I know that the wheelhouse scene in Splash is from America Sings. Another goose from there is in the Star Tours queue.
Good morning, son
In twenty years from now
Maybe we'll both sit down and have a few beers
And I can tell you 'bout today
And how I picked you up and everything changed
It was pain
Sunny days and rain
I knew you'd feel the same things... sigpic
Not that scary. They essentially just look like they've been turned off. Although there was that one morning I was walking through the finale scene in Splash and one of the chickens on the showboat was shaking her hips back and forth.
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Some are left on, some are turned off.
Generally speaking, hydraulic AAs are able to be tuned off, and have that ability enabled on their control panels. Pneumanic AAs are a bit more complicated to shut off, since their systems weren't made to be cycled regularly.