They didnt seem to do that when I was with SKY.
The username and password stored in the router appeared to be generated from the MAC address but there was no sign of them knowing the MAC address of the router they had sent.
Of course, they have every opportunity of recording the MAC address of the router used and the user name and password used at login time if they so wish but if so it does not seem to cause any issues.
BT Infinity 2 - IP profile 77 / 20 - super fast!
Previously BE Unlimited - 21,000 Download 1,200 Upload but then moved house - 6,500 Down, 1Mb/s up - gutted!
Ex <n>ildram , been to SKY MAX - 15,225 Download