Technically any charging of a Lithium battery is "bad" for its health. Batteries are usually rated for a certain number if charge cycles from the manufacturer and after that number of cycles will start to lose capacity. The best advise I've seen regarding battery health is to keep it from charging to %100 everytime. As others have stated, the charging speed can also have an impact as it creates heat and heat will also wear out the battery.
As for your specific device it seems like it's consuming more power than the charger is giving it, so even when plugged in and turned on it may be discharging the battery still as it's not getting enough power. Either you buy a new charger that can put out more power or you turn it off while charging it. Either case shouldn't be bad for the battery health.