I have old g3s running 8.6 connected by ethernet cable that works just fine. Any ethernet device will work through a router via cable. Even my old G3 laptop running OS 9.1 connects just fine wirelessly (but of course not in n mode).
If the router has its own config/control software (like the apple products), it may require a more modern OS. I think the new TCs require 10.5.+. Most other routers are configurable by web page. But as someone said, the manufacture often draws a line on what OS they answer questions about.
I can configure my modern actiontek router with my 2002 vintage netscape browzer on my OS 9.1 laptop for example.. but I wouldn't expect actiontek to answer OS specific questions.