I agree that you should take the expanded battery out and arrange to have it recycled.
In a desktop computer, the DC power supply contains large capacitors to smooth out the DC power supplied to the chips. In a notebook computer, that job is performed by the battery. You can certainly bench test the computer with no battery, and it will operate that way.
it is not prudent to run a Notebook computer without a battery for day-to-day use. No battery means no buffering of DC power, which may leave your notebook computer exposed to damage from power fluctuations.
Question: the battery of my macbook pro has been expanding severely. the trackpad does not work anymore.. it is a 2011 model. any chance Apple would replace the battery free of charge?