I think it does if the add new hardware wizard runs and you tell it to check the Internet, but it only looks for Microsoft drivers which have not been updated for many years. . .
I had no luck with Windows Update providing drivers for Win 2K after their support ran out in the summer of 2010.
However, there are many driver discs on eBay for PC's that ran the OS, and some OEM's still have them for download. I know that Dell & Lenovo (IBM) does, don't know about HP.
As an added note, there was an "unofficial SP5" for Windows 2000, that will give you some added updates, including having IE6 w/o having to install it from the go. You can either add it to your original install disk, using nLite, or you can just download & click onto the .exe file, and the SP will install.
This SP was written by MS, was considered for release, but wanting to push XP at the time, they decided not to. I have it on all 3 of my 2K installs, and they all run better with it installed.
Now, if only a "unofficial SP4" will emerge for XP, that would be great!