there is no need to take the battery out when using the power supply, to be honest i don't even know if it would work, but i doubt anyone would recommend you try it as then the back is open to the elements.
whilst using the power supply if the battery is over 90% the battery is bypassed and the laptop works straight from the power supply. if you primarily use your laptop from the power supply then i would advise calibrating the battery at least once a month. This just means running it through one complete cycle of running the battery down and then charging it up again fully. there is a guide to this opn macrumors, if you do a quick search.