There are no automation preferences in my Logic 6 Express that I can find. And I've never
been asked if I also want to move the automation. (that I remember!)
Put some track automation on a region. Then move the region a few bars and it should ask you if you want to move the automation (I think its gives you the option to always move automation, or never or ask) and this is changeable in the prefs too. If it doesn't ask please report back what it does. Put some distinct hills and valleys in the automation so you can see if it moves or not.
Actually what I really want to know is, Can you add a bar anywhere - say bar 43, without
messing up the automation and tempo changes - Or for that matter subtract a bar. That
would be handy too at times.
You need to do a little experiment to determine the answer to that. It would probably work if you cut the region into two, then move one (where automation moves with it).
This is why I said I don't mess with automation at all untill the song is finished. If I am going to change the arrangement and move things around and add bars, then it becomes much more complicated with automation.
The other thing you can do is to output the tracks to new audio files (which I THINK will record the automation to the new files). Then you don't have to mess with automation - but its not editable of course.