If the G3100 hooks up to the Verizon network through a LAN cable instead of coax does it need to still be a cable modem or can I now use any good compatible wifi router?
FiOS does not use modems. It uses routers. The Verizon routers, G3100 included, are just routers with a few additional features. These features include integrated MoCA, control from FiOS website and app, the ability for Verizon support to remotely mange and specific networking features for Verizon set-top-boxes.
You can use any router you want, however if you have Verizon set-top-boxes they don't work as well or at all with a non-Verizon router (depending on box model). Further, Verizon doesn't provide any support past the ONT when a non-Verizon router is used.
If you don't have Verizon set-top-boxes, it's easy to use a non-Verizon router. You'll likely not need Verizon support as FiOS is very reliable, but if you like having them available stick with a Verizon router or keep one around to plugin when needed.