Will my MacBook work if the battery is disconnected?

My MacBook is dead. It does not power on nor does the AC adapter charge the battery. I believe that the battery is not working.

So the question is, will it power on with the battery disconnected and the AC adapter plugged in?

Or does it need the battery connected to turn on?

P.S. I want to get my data off of it, before I turn over my laptop to Apple for battery replacement.