i am on fi. first invites. sad to know i did not make that point clear.
yes you can disable cellular data. the phone can work on wifi only. at that point if you keep cellular OFF, the phone will seek out wifi networks and connect to open ones that meet their strict guidelines.
how good or bad that experience is depends on the network you are connected to. google fi doesn't do anything magical to the network, it just connects to it after it has verified its been deemed secure. if it is not on googles list of secure networks AND you can connect to it (eg. you already have the credentials or its a free spot like at starbucks, etc) you can still make calls but they wont be secure.
if you go to a friends house who has wifi and you already have their login credentials to access their site, you can use wifi there. fi probably wont even know the site so it will not play in setting it up.
if i left something out, let a brotha know.
if you only want to use the phone on wifi only, you dont need fi for that. use google hangouts, skype, whatsapp, or any of a number of voip calling apps avail to make free wifi calls.
if you DO have fi and are on wifi only, AND fi sniffs out a secured wifi network to vpn to, that would be the only difference over using a standalone voip type app.
my experience is this: i have not had any lag or echo type calls or robo voice sounding calls or gibberish calls.. all of my calls have been just fine. i use wifi probably more than cellular since i am around wifi nearly everyday and the calls are crisp as your business suit shirt after you get it from the cleaners...
clear as mud???