Usually it has been seen that people who use laptops actually plug the laptop to the power supply. However this edison battery is the wrong way of charging the battery. You should charge a battery once or twice a month. The battery should be charge fully at least 30 minutes before you start using it. In case you are going to use direct power supply, then it is best to remove the battery. This will ensure two things -- first, the battery since it is charged already will not discharge uselessly and second, it will ensure that the battery life is extended.
The battery will over-charge if left attached to the charger. The battery stops charging automatically when full lithium facts so it will not over charge. If the battery is left on charge too long it is possible that heat will damage the battery.
OLithium Ion (Li-Ion) - This was the latest battery technology before lithium polymer. They have a higher power density than NiMh and NiCd batteries. Li-Ion batteries generally come standard with most phones. For most people, this battery technology represents the best combination of size, capacity, and value. These types of batteries don't suffer from the poor memory effect and can be recharged anytime.
Avoid using replacement that has been on lithium bettery stock for a while. During storage the battery can lose much of its capacity through internal resistance, which damages it and lowers the maximum capacity.
The only drawback on this type of lithium based battery is the high cost. Since it is expensive, it makes sense to use it the right way to extend its service life.
The bottom line, be gentle to your lithium-ion batteries. If you excessively charge the battery, with high voltages, and heavy load conditions, it will shorten your battery's life. It's best to charge at a slower rate.