There really isn't a need to remove a ThinkPad battery to increase its lifespan if you follow the guidance in the "How can I increase battery life?" article, unless you use the ThinkPad in a hot environment.
If you do decide to run with the battery out:
Store the battery in a cool area.
About once every three months, attach the battery to the system to let it charge to 50%. The battery will slowly lose charge in storage. This is normal and the charge is recovered once the battery charges back up.
Your system may run slower. The power adapter and battery together form the power delivery system for your notebook. Removing the battery reduces its ability to support heavy loads, so the notebook throttles back the maximum CPU speed. In some cases, changing to a higher wattage power adapter may eliminate this throttling.
There is a higher risk of system corruption or damage through accidental disconnection of the power adapter.