Laptop batteries have finite life spans. Whether you use the power cord and remove the battery it will lengthen the life of the battery.
Li-Ion laptop battery lifespan is approximately 1000 charge cycles, or 2-4 years under normal operating conditions.
Keeping the battery in a cool place can prolong its life but not in a period of extended storage. The Li-ion battery should be stored at 40 percent rather than full-charge state.
The battery ages even if not used. For best results, keep the battery cool. In addition, store the battery at a 40 percent charge level. Never fully charge or discharge the battery before storage. The 40 percent charge assures a stable condition even if self-discharge robs some of the battery's energy. Most battery manufacturers store Li-ion batteries at 15°C (59°F) and at 40 percent charge.
Keeping a laptop battery on constant charge is and never using it is not good for the laptop battery. Run the battery down and recharging it at least once every month.