The connection from the ONT to the router is part of the outside connection and not part of your network. Essentially, yes it can be done but that is the only thing you could use the powerline for. Your internal network would have to remain completely separate.
You may lose speed. It depends on how good the house wiring is, how good the powerlines are and how fast the connection was to begin with. With the lower speeds, 300Mb/s say, I suspect you may be alright.
Edit: typing at same time as Licquorice.
