One strange thing though is that there is power to the lighter and the dome light even when the key is not in the ignition.
I up this thread because I'm wondering the same question. The answer seems yes from what is said here but that definitely unusual.
Seems normal to always have power to the dome light and inspection light but I was surprised to see the cigarette lighter always on.
Was very happy to have a functioning cigarette lighter for the first time in decades so I bought a nice socket with usb plugs and voltage reading.... That may not be a good idea if it draws constantly on the battery.