I assume it is indeed a simple pass-through, so functionality in DOS will depend on the sound device on the laptop itself. You would need whatever driver is needed (if any) to get the sound card working, but you should not require a special driver to use the port on the port replicator.

As the owner and now regular user of a Toshiba PA2717U docking station, I can confirm it's a simple pass-through device, so no drivers are needed for it.
.
This is because most (all?) of the interfacing chips are already built in the laptop itself, and the station is just a set of headers for them. Just ensure that the yamaha setupsa.exe program or another suitable driver is loaded for the sound hardware and you're good to go.
.
When you boot the laptop, you will get a POST/BIOS message stating that the port replicator is attached.
.
I've tried it on my 460cdt satellite pro, and it works great with the gravis dog bone pad, quickshot starfighter, quickshot python, wild-things premier pad and interact propad 4.
The only problem I've found so far with it is the MS sidewinder 3D pro joystick, which gives erratic readings on the analogue in either mode. And I've not found this elsewhere.