Verizon FiOS and Google Wifi

I am contemplating getting Google Wifi for a meshed network.  I read a previous thread on it.  Here is my thought....  I have FiOS with TV and Phone.  Could I simply set up Google WiFi as a Sub LAN on my network.  In other words, use my router as the bridge to the network and have Google Wifi give out a different set of IPs.  My FiOS router gives out the 192.168.1.XXX IPs and the google router (plugged into the router) then gives out IPs like 172.28.100.XXX