It's up to your hardware. I have an older toshiba laptop that has a built-in ethernet and one that is on the docking station. They both work if you plug it in (depending on your network). and they each have their own MAC address. When I plug in one and wait, that computer gets one IP Address, when I unplug that and plug into the docking station, then it gets a different address because my DHCP server thinks its a new machine because the DHCP leases are based on the MAC address.
It depends on the hardware really and whether the ethernet port on the docking station is a "new" device vs a "passthrough" device.
On Windows, open up the command prompt and type "getmac" and it'll tell you the mac addressess. You can also dock your computer and type in "ipconfig -all" and it will show you all your ethernet ports and their mac addresses.