Should the MacBook turn on without battery?

I am thinking about getting an old macbook for studying purposes only, and there is one guy selling a macbook in a good condition. He says, however, that the macbook turned on when it had a battery, but he had to throw it away because of swelling and now it doesn’t turn on anymore.

Also, does the green led on the magsafe charger indicate that the logic board is working fine?

It is a macbook 13” 2009 unibody