The "Automobile Adapter" indeed is only a switching power supply. I still own mine, with the proprietary Compaq connector chopped off. It's laying in my junk drawer and inside is guest a boring switched step up converter.
It could connect to the docking station just as easy as to the laptop itself, the connectors are identical on both.
It could connect to the docking station just as easy as to the laptop itself, the connectors are identical on both.