Old "Hand built" system with a Pentium IV processor (Circa 2000) which WAS running W2K runs W7 32 bit just fine. Onboard memory just 512KB but it runs.
It's definitely not as fast as W2K but it DOES work satisfactorily. Remember we are talking about a 10 - 11 year old piece of gear which is a Geological age in computer terms.
The ORIGINAL OS definitely DOES run faster faster on this particular bit of kit (W2K later was copied as the basis of Windows 2003 Server which still in my view was MS's BEST SERVER OS ever including W2008 Server) but of course W7 has far more complex hardware and operations to deal with so probably NOT a fair comparison.
Even running W2K as a virtual Machine will surprise many of you who have never experienced this OS -- definitely one of MS's better efforts and FAR superior to the original Windows NT which we used to call Windows Neanderthal or Windows No Thanks.