"Does the Bluesound node need to be hardwired to the extender or does the Bluesound virtually "pick-up" the WIFI"
No and yes.
No and yes.
I'm assuming you have gone on the Bluesound website to follow their instructions to allow your Node to connect to your network. That done, it should "see" it once turned on. The light is initially red, then turns green while searching, and finally blue when connected. If an ethernet cable is plugged in, it will defer to that and connect to your network immediately showing the blue light..
If your network doesn't reach your listening area, then yes, a good extender will bring the Wi-Fi closer to your system and the Node should be again set up via their website to "see" the "new" network created by the extender which will have the same name as your primary one but with "_EXT" following the name meaning that you are now on the extended version of your network. This will require your password (router Key) again.
I actually dealt with this the other way around by moving the router downstairs near my listening room and ran an ethernet cable to my system. Then I installed a NetGear extender upstairs for our computers which run via Wi-Fi.
Hope this was helpful, Fred