All the laptop batteries now are lithium-ion. They last longer when they are kept at full capacity, constant draining and full recharge cycle reduces their life.
However you cannot "overcharge" them because inside the battery module is a chip that controls how much they are should be charged anyways.
Yeah, "overcharging" the battery would require disassembling it, bypassing the interface circuitry, and then connecting it to an inappropriate power supply. Which is not the kind of thing that's likely to occur unintentionally.
That said, if you were to actually do that, I'd expect the battery to be damaged, and then fail (possibly explosively).