No, my unit is actually "either connect" as it is installed, and as it is DESIGNED to be installed in a car, it is wireless.
And it is 12 volt.
I do agree however, due to the way power systems are designed, it is more efficent to use the 120 volt wall wart,, actually all the time, if it's six volt
Converting from12 to 120 volt you loose about 10%
Converting from 120 to six you loose about 10 percent (Total loss 19%) or more depending on how the wall wart is designed, but odds are not more than 25%
Converting from 12 volt to six volt, by the normal method, you loos at least fifty percent.