I always leave my laptop plugged in, and every month, drain the battery to calibrate it. I have never had an issue with doing this at all in many years.
Leaving your laptop plugged in with the battery does *not generally* cause it any harm - I am not sure where the Apple tech is coming from here.
The problem with charging your battery and then plugging it out, using the charge and then charging it up again and repeating this behaviour as a continuous thing is that the battery will not last long, because any rechargable battery only has so many charge cycles.
If you do it that way, you are going to be at least charging the battery 5 times a week (if you use every day) - if a battery has, for instance, 100 charge cyles before a new one is needed, in 20 weeks the battery is going to be ruined.
If you charge it once a month, you are only using 12 cylces per year - meaning a much longer lasting battery.
Currently, my G4 powerbook is 2 years old. It has lost a mere 6 per cent of it's original battery capacity over almost 24 months, according to
COCONUT BATTERY
So running your laptop with the power plugged in *should not* cause any issues at all, providing you remember to run the battery down at least once a month to re-calibrate it.
I have another laptop that still has its original battery in after 6 years using it plugged in all the time too
I will add though, that I always use good quality surge protectors, because a surge can damage the battery if your laptop is plugged in - even kill it, and if your sockets are prone to spikes, they can also damage it. Using a good surge protector will help eliminate any damage in this way