The device you've linked isn't a modem. It can't connect to a phone line directly. There is no Cat 6 connection on an NTE - are you talking about an Openreach modem?
The router you've mentioned has no way to connect to the phone inlet of a modem without a weird cable and definitely no way of providing the VDSL signal a regular modem is expecting to see.
The SamKnows box has no way of sending data if it's sitting between an ISP provided router and the phone line. It doesn't know your username and password or how you are connecting to the network, IPoE, PPPoE, etc.
Maybe I'm just misreading this but the scenario you've posted makes no sense. SamKnows kit are routers running SK software. They don't report on customer traffic they monitor for 'quiet periods' when they can run their tests without having other traffic ruining it, and they certainly aren't double-sided modems that take signals from the phone line, do their thing, then repackage the phone line for delivery to the ISP-supplied modem.