Maybe not damage it, but it will reduce its lifespan somewhat.
The guidance is to never leave the battery in the notebook if you are always going to have it plugged in.
So, if you are like me, and you usually have the notebook plugged in at one location, then every two weeks, unplug it and run it off the battery until you get the low battery warning. Then charge it up again.
There are times when I move the notebook around, so I wouldn't want to have to keep installing and removing the battery.
That could cause problems too, if you break the latch that secures the battery to the notebook.