I am no expert in this field, but from what I have been told, YES, they will see the mac address of your router, but ONLY that one device. Everything you connect to it on YOUR side of the router "should" be hidden from them. That is the way my ISP operates. My cable modem assigns an IP address to my router, and as far as they know, that is the only device attached to my modem.
Sometimes I wonder whether the world is being run by smart people who are putting us on
or by imbeciles who really mean it.