The amount of power required to run the laptop and charge the battery due to inefficiencies of charging circuit, conversion from 110v -> 18v or whatever its using, etc would more then likely outweigh any benefit of just leaving it plugged in. Simple test would be to get a good power meter, run it for a week constant on, record the usage, reset the power meter, and run it while turning it off and on and measuring it again.
With the above said a rechargeable battery can only have so many charge/discharge cycles. While it is recommended to occasionally discharge and recharge to keep your battery healthy each cycle does slowly kill your battery. In general a laptop battery starts dropping below 100% max charge after around 200 - 400 cycles. If you are cycling on and off you will not be able to fully charge it in 6 months since you probably are recharging 3 - 4 times a day? And since it now holds less charge your are cycling more often and its a downward spiral. Your battery won’t hold a charge at all in less then 18 months, maybe 2 years if your lucky, and the cost of a new battery far outweighs any possible energy savings.
Fun reading: https://www.guidingtech.com/66018/keep-laptop-plugged-in/
Old site but has actual power draw numbers: http://www.humaninet.org/laptop.html