Yes, it will give the battery a shorter lifespan.
In the manual it will say to make sure the battery is fully discharged before recharging it. If you always have the power supply on while the battery is in it will give the battery a shorter lifespan.
So make sure the battery is out when using the power supply.
My sis has a laptop and she did that all the time, now the battery is officially knackered, it doesn't even last a full minute without the power supply plugged in.