You sure can have a Wireless repeater on the network using the existing Cat 6 wire. On my FiOS setup I currently have 3 different wireless repeaters all thoughout the house, no issues.
I can probably find you a guide, would you be able to provide the model of the Netgear router you would want to be using as the repeater? Most routers universally support being a hotspot, and generally the steps are:
Disable the DCHP server on the router going to be the repeater
Make sure the WiFi SSID and Password are the same (This is optional, and you can have two seperate WiFi signals, but for convience its best if you use the same information as your main router so your devices will seamlessly connect depending where you are in the house).
Now, plug one end of the Cat6 cable in your wall to one of the yellow "LAN" ports on your FiOS router, and then on the other end plug into a "LAN" port on the other router.
9 times out of 10 this method will work, although I can be more specific if I had the router model.