That's really hard to believe, especially for any kind of professionally-built cab.Because power doesn't disappear. It just gets used in different ways. In the case of a variable L-pad on the tweeter, if you turn it all the way off, the L-pad is 'soaking' up the power that was meant for the tweeter in the form of heat.
Doesn't the L-pad present a very high impedance to the circuit, like 50 ohms or something? That would "shunt" basically all the power to the 8 ohm speaker load instead.

What would be the point - why would you want something like that?