Can a Macbook Air work without battery?

It’s common for a normal pc notebook to work plugged to power but with no battery; I have a macbook air with a broken battery.

Since the battery is not user removable (sort of speak) and its a relatively new notebook, probably it was a short-circuit caused by the charger; we’ve replaced it, but the battery still doesn’t charge, so it is like the battery was gone; my question is: If I remove the battery for testing, can the Mac work normally? does it maintain memory, cache or time?