This information pertains to LabQuest 2.
The original LabQuest and LabQuest 3 do not have this functionality.
LabQuest 2 with Lab Armor installed will not fit in the LabQuest 2 Charge Station (LQ2-CRG). However, it is possible to remove the Lab Armor easily. There is also access in the Lab Armor to support the AC adapter if you want to leave the Lab Armor in place.
The new model charging station does fit the LabQuest 2 without removing the armor: LabQuest® Charge Station (LQ3-CRG)
See also
Will my LabQuest Charging Station also work with the LabQuest 2 and LabQuest Stream?