Is it safe to operate a laptop without battery?
Solution 1:
Longevity of a notebook has many factors, but power through motherboard circuitry while sleeping/hibernating would rank near the bottom of the list in my humble opinion. The limited amount of voltage/amperage traversing the components while in that state should have no effect on the lifespan of your machine.
Most of the time motherboards are not high failure items, unless you get a bad batch and/or poor quality throughout production. In my experiences, plastic pieces are the first to go, lid latches, the lid itself from flexing on open, hinges, case bottom from heating and cooling, etc. With daily use and even the best care these pieces still break on a more regular basis than a motherboard that is always receiving power.
Also of note: A recent thread on the Linux Thinkpad Mailing list was discussing a development with Lenovo notebooks and the 65W Power Supply units. Main point was that the 65W adapter with the added power of the battery was not sufficient for high intensity loads and could easily damage the motherboard, hard drive(SSD), RAM. Suggestions were to not use a 65W brick at all(use the 90Ws) and to also leave the battery in, it was designed that way. :)
So, unless you are absolutely certain that your notebook will never use over the power stated on your brick, I would leave the battery in period. You may well end up doing more harm than good.
Thread is located here
Solution 2:
In general, you should be fine running a laptop off of only AC power. The only issue with it would be when you're using "dirty" power, but that's not a problem for pretty much any industrialized country or region now-a-days.
Disconnecting a battery when it's fully charged can help extend its useful lifespan, as well as the single charge time. However all batteries degrade over time, and the extent to which disconnecting it will help is very dependant on the type of battery, amount of charge on it, and numerous other factors. Following the manufacturers recommendations is probably your best bet.