The answer is YES. Most laptop manufacturer recommend to remove the battery if you are using power chord. This will increased your battery Life Span because like any other electronic device which will defect sooner or later with continuous usage.
It is recommend to keep your battery charged periodically (Once a week) to keep it functioning well. If you charged it at 100%, when you plug it again (a week later), do not be surprised if the charged percentage deplete. It is normal for a battery to deplete 10% – 20% without any usage.