I can't understand what you're asking. Lets see.
"If I have a wireless router extender that has a LAN port and this router is linked to my primary router, "
Ok so you have a Wifi range extender basically. You're taking a wifi signal and rebroadcasting a wifi signal for better range. We don't extend routers. One router per network only!
"if I plug a device into the LAN port on the wireless router extender, it that equal/equivalent to plugging directly into the primary router?"
It could be! you'll have to test it to see. The wifi range extender might disable that port to prevent gaining access to the network. For example: If you didn't have a wifi password you could in theory plug in and gain access which would be bad for an unmonitored public access point.
It could certainly work though! Depending on the model of extender, it may have a Client mode. In which case that port WOULD be like connecting directly to your existing network. In client mode the extender acts more like a bridge. Connecting the two points together with a wifi bridge.