I installed it without. I just made sure that the battery was fully charged. Ised the battery a few times until it was about signalling it was at half power, recharged, reused, recharged and then I installed the firmware without any problems.
I have however had problems getting any images off the camera on to the computer. I was able to at first but somehow its no longer allowing me to do that. However you can get over that problem by using a card reader. Personally I don't see the point in buying an ac adapter at $99 or £50 if you will only use it rarely.
You can get a way without upgrading the firmware until you are certain that the battery is strong enough to take it. Err on the side of caution.