No, Now a days Laptops are coming with Li-ion cells so there is no problems to overcharge it, and also in all new laptops have the feature that when the battery got fully charged it will not take more charge inside.
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The Lithium-Ion battery which are most commonly used in laptops, don't need to be drained and recharged. The biggest effect comes from heat. If you use your laptop continuously for a long stretches of time it overheats. In those scenarios it's recommended to remove the battery and use the laptop plugged in.