No bitcoin will be always conneted to fiat,even if goes mainstream,as you cant save anywhere bitcoins ,it may happen in the future this option but i really doubt,bitcoin will be dependent always ,and we cant do nothing to stop it as we need our fiat as well.
I also agree that bitcoin will always connected to fiat/other currencies as all other currencies are connected with each other but I think it alone for virtual system will in a time remain independent.