Extender mode - will it bridge LAN port?

If you enable extender mode , will the ethernet port act as a LAN port ?

So I have a wireless network I need to connect to, but my device only has ethernet. Can I use these routers in extender mode and connect the device via the LAN port, where the router acts as the wireless client?

Yes. The LAN port will be bridged to the main network in extender mode.