Do you connect the charger in the MacBook Pro battery damage if using device ?

Provided you are using the correct charger for your Mac (13" have a 65 watt charger, 15" and 17", an 85 watt charger), it has enough capacity to power the computer for normal tasks, and the leftover power can charge the battery at the same time. If you are doing something very intensive, there may not be leftover power, but the Mac will take power from the battery if needed. Once the battery is fully charged, the pilot light in the charger plug will change from orange to green and no further charge will be applied to the battery.

You can use your Mac plugged to the charger with no damage to the battery or the computer.