Your suspicion is wrong. The check to see if the batteries are dead is simple. Touch both ends of the tool and you will get a green light.
Touch just the line conductor (but not the end of the tool) and you will also get a green light.
While, or before, touching the line connection you will get both green and red
Touch only the neutral conductor (but not the end of the tool) and you will nothing
Touch the end of the tool while, or before, touching the neutral connection you will only a green light
So you require a light to show to know that the battery’s have sufficient charge.
No light means dead, or no, batteries
it is possible, I don’t know because my batteries are charged, that with dead batteries you will get a green from the line connection without touching the back of the tool. With dead batteries you will get nothing from the neutral connection.