Performance is degraded when the battery is removed and the machine is running only on the AC adapter. Apparently it was designed this way.
Leaving the battery in and running from the AC adapter does not harm the battery and Apple recommend that you occasionally remove the AC adapter and use the computer until it shuts itself down through lack of power.
As a matter of interest, all batteries have a life expectancy which is usually measured in charge cycles. All batteries will die eventually, even if you do not use them.
Even without the battery, but with the AC adapter plugged in, the date and time should be maintained correctly. System Preferences > Date & Time has a setting to use a Network Time server which keeps the clock up to date. If you remove the AC power after shutting down the computer and the Date and Time gets lost, you may have a problem with your backup battery.
I use my mac mainly on my desk and as such the power adapter is always readily available. I have been charging the battery, then removing the charger and running off of battery power until it is drained. This will eventually kill the battery, so now I am running it without a battery.
Firstly, are there any performance/longevity issues I should be concerned with? I know the power management system uses the battery as a sort of fail safe against internal circuit overloads... I don't know if that is still the case with newer computers.
Secondly, is there any way to have the computer automatically update the date and time? Every time I start the computer I get the warning screen that says the date has been reset and this may cause programs to act weird.
Thanks for any help!