battery removed from macbook, will it continue to operate if unplugged

My very old Apple macBook, OS X version 10.9.5 was put into storage when the battery began expanding, presumably leaking a chemical or more...

Now, after 4 and a half years, I have begun to use the laptop; I plugged it in and it was updated.

My concern is: do I have to keep the computer connected to an electrical outlet at all times?

My granddaughter is coming to stay with me. She will be taking online classes and I would like this old computer to be available for her to use.

Thank you.