"Would you say this is also true for other doubles as well?"

I don't think there is a universal rule on this, but varies by make.
With a Lefever for instence it makes absolutely no difference whether the gun is cocked or uncocked in putting it back together. This applies to both extractor guns & ejector guns eith the in-frame ejectors (the vast majority of Lefever ejectors). I can't speak for the few with forend ejectors as I have never even seen one of these.

Miller/TN
I Didn't Say Everything I Said, Yogi Berra