Wasn't aware that Sky are giving away free calls to 0871. BT and a few others include 0870, but this is the first I've come across an inclusive 0871. In any case, they're still not the best at answering the phone...only last week Watchdog reported a call that went for 2.5hrs unanswered.
As for phone-line being connected, it's the multi-room which is the issue, not HD. If you have premium channels (e.g. sports, movies) and multi-room, it's a condition of contract that all the boxes have to stay connected to the same phone line. And yes, they do check it. Reason being it's to ensure that you don't take a multiroom subscription (at £10 extra) then lend the extra card to friends or family (who would save considerably more than £10 versus paying for premium channels). If you're caught without all boxes on a multiroom subscription not connected to the same phone line, you'll first get a warning letter then charged for N x premium subscriptions.